The Second XI completed a two-day, treble victory over the Unicorns by winning both T20 fixtures at Burnopfield CC.
Bowling first in the first game, Durham restricted the visitors to 105/6 from their 20 overs.
The returning Chris Rushworth took 1/19 from his allotted overs but the two spin bowlers were the stand out performers.
Gurman Randhawa took 1/13 and Adam Hickey 3/18 before Durham chased it down with consumate ease.
Graham Clark smashed 70 from 26 balls, including 8x4s and 4x6s, as they reached the target within eight overs.
Batting first in the second match, Durham ended up all out for 159 thanks largely to Phil Mustard's 80 at the top of the order.
In reply, the Unicorns fell short on 130/8.