Result: Durham (217 & 359/7d; Latham 119, Clark 86; 8 points) drew with Kent (206 & 184/9; Billings 70*, Northeast 67; Weighell 3/51; 8 points)
Graham Onions became Durham's leading first-class wicket-taker but Sam Billings made an unbeaten 70 to deny them victory in a thrilling Specsavers County Championship match at Emirates Riverside.
Starting the innings two shy of breaking Simon Brown's record after his first innings six-fer, Onions struck with his very first ball to draw level with the former seam bowler.
There were six overs left by the time he had overtaken him, trapping Adam Milne LBW, Durham required only two more wickets for a brilliant victory.
James Weighell then removed Imran Qayyum in the penultimate over, but ex-Durham man Mitch Claydon saw out the over & Billings blocked out the final six balls from Onions to seal the draw.
It was the second time this season Kent have finished nine down against Durham, with Matthew Potts denied by Yasir Shah in the final over at Canterbury earlier in the season.
Durham's unbeaten Specsavers County Championship run now stands at seven matches with two games of the 2017 season left.
Set a target of 371 in 56 overs, there were 28 overs left when Billings went in at 74/5.
Kent skipper Sam Northeast followed his 110 out of 206 in the first innings by making 67 of the first 112 runs.
He was sixth out, inside-edging a drive at Keaton Jennings into his stumps, with 15.2 overs left.
After passing 1,000 championship runs in the morning, Paul Collingwood batted on for 7.3 overs to add 62 after lunch before declaring on 359/7, and Kent soon lost both openers without a run on the board.
Onions struck with his first ball, having Sean Dickson caught behind and in the next over Daniel Bell-Drummond went the same way to Chris Rushworth.
On ten, Northeast edged Rushworth past Collingwood's left ear at first slip and had progressed to a 69-ball half-century by the time Billings joined him and played a few shots of his own.
In the morning, Tom Latham completed his second century in three games for Durham.
He survived a sliced drive to Joe Denly at gully off the luckless Milne on 65 and was becalmed in the 90s, tied down by Claydon before a back-foot four through the covers gave him his 13th four and took him to his hundred off 221 balls.
After resuming on 49 Graham Clark progressed solidly to 86 before skying an attempted pull off Claydon to end a stand of 180 and bring in Collingwood, who got off the mark by driving left-arm spinner Imran Qayyum over long-off for six.
On 20 he lifted the same bowler to the mid-wicket boundary to reach the 1,000 target, but was bowled for 35 when he went down the pitch to Qayyum.
In the post-lunch thrash Latham departed for 119 when he was caught one-handed above his head by the 6ft 6in Zak Crawley at extra cover.
Ryan Pringle hit an unbeaten 30 off 23 balls and the declaration came when Mark Wood was bowled by Denly for 24.
When Wood had Crawley caught behind with the second ball after tea he looked a possible match-winner.
But Durham were unable to force victory and extended their unbeaten run ahead of Sussex's visit a week on Tuesday.
Close, Day Three: Durham (217 & 145/2; Latham 64, Clark 49*) lead Kent (206; Northeast 110; Onions 6/62, Wood 3/48) by 156 runs
Only 29 overs were bowled in three sessions on the third day of the Specsavers County Championship match between Durham and Kent at Emirates Riverside.
Durham advanced from 57/2 overnight to 145/2 in their second innings, leading by 156 with Tom Latham on 64 & Graham Clark 49.
Both profited from the absence of wicketkeeper Sam Billings, who was still troubled by a migraine.
His original deputy, Daniel Bell-Drummond, missed a difficult chance offered by Latham on 40 then Joe Denly took over and dropped Clark on 25.
Adam Milne and Darren Stevens were the bowlers to suffer, but Kent generally did not apply enough pressure, especially when play began on schedule at 10.30am and they failed to make the batsmen play often enough.
Durham added 17 in 30 minutes before rain arrived, but the batsmen were more fluent when play resumed at 1.25, adding 26 in 25 minutes before bad light intervened, despite the lights being on.
There was more rain before a 4.05 resumption and Latham immediately cut Stevens for an all-run four on his way to 50 off 122 balls.
At 4.55 it was again decided that the light was too poor and play was abandoned 30 minutes later.
Close, Day Two: Durham (217 & 57/2; Latham 27*; Haggett 2/12) lead Kent (206; Northeast 110; Onions 6/62, Wood 3/48) by 68 runs
Mark Wood hit his highest first-class score before Graham Onions closed in on a club record as Durham finished 68 runs ahead with eight wickets in hand against Kent at Emirates Riverside.
All out for 206, with Onions taking 6/62, Kent trailed by 11 runs on first innings after falling from to 134/3 at tea to 175/9 shortly after it.
Durham were also indebted to the all-round efforts of Wood on his comeback from the heel injury which had sidelined him since the second Test against South Africa in mid-July.
His career-best 72 not out rescued Durham from 77/7 in the morning and he followed up with 3/48.
He shared an eighth-wicket stand of 106 with James Weighell, who made 55 before Mitch Claydon took the last three wickets to finish with 5/54 on his old stamping ground.
In recording his best figures for two years, Onions was on the mark from the outset, pinning Sean Dickson lbw then beating Joe Denly's forward defensive push to take out the off stump.
Northeast went in at 14/2 and got off the mark with an edged four when trying to withdraw his bat, but sped to 50 off 45 balls with ten fours, despite losing Daniel Bell-Drummond, who grafted hard for his 26, only to surrender when he tried to pull Wood and lobbed a catch to mid-on.
Starting with the second ball after tea, Kent lost five wickets for 13 runs. Zak Crawley was lbw to one from Wood & three balls later Darren Stevens hung out his bat and edged behind.
Left-hander Calum Haggett pushed limply down the wrong line to have off and middle rattled by Onions and the surrender continued as Adam Milne edged a lavish drive. Sam Billings, suffering from a migraine, went in at 147/7 and departed first ball, having his leg bail trimmed when aiming for mid-wicket.
Claydon clubbed three fours in contributing 16 to a stand of 28 before driving to deep mid-off to give Onions his sixth wicket.
On 81 when last man Imran Qayyum joined him, Northeast farmed the strike and cut Wood over backward point for six on the way to his 102-ball century, which included 17 fours.
He finally fell when he edged a forcing back-foot shot off Weighell to give wicketkeeper Michael Richardson his third catch.
With Billings resting, Kent emerged with Bell-Drummond behind the stumps and he held the catch off Haggett which removed Keaton Jennings for 13.
Haggett also brought one back a long way to bowl Cameron Steel, shouldering arms, for nought.
Close, Day One: Durham (61/4; Milne 2/14) vs Kent
Four wickets fell in the 32 overs that were possible on Day One of the Specsavers County Championship match between Durham & Kent at Emirates Riverside.
Ex-Durham man Mitch Claydon & New Zealand international Adam Milne managed two wickets apiece as Durham finished on 61/4 at stumps.
Sharp catches by Sean Dickson at second slip gave Claydon both his victims, the first being Keaton Jennings, who had dug in to make 17 from 67 balls.
Kent dispensed with the toss after rain prevented play until 4pm, but under clearing skies they kept the hosts pinned down with some tight bowling from the seam bowlers.
Durham had reached 35/1 in the 24th over, but then lost three in five with Paul Collingwood departing for 11 when he edged an excellent ball from Milne to Sam Billings.
With Claydon extracting good bounce, Keaton Jennings fell to a back-foot shot and two overs later Cameron Steel's edge was held at head height by Dickson.
Opener Tom Latham was off the mark first ball with a square-driven boundary off Darren Stevens, but added only four runs before he was out when half forward looking to turn Milne to leg.
Stevens got past the bat a few times in an eight-over spell before making way for Claydon, while Calum Haggett was out of luck when Steel survived a sharp chance on five to Joe Denly at third slip.
Milne returned for a second spell and found some away movement off the pitch. Collingwood, needing 35 at the outset for 1,000 Championship runs, edged a snorter behind.
Graham Clark & Michael Richardson were the unbeaten men & will emerge on Day Two looking to add to Durham's overnight total.