Their third successive win kept alive the visitors’ hopes of snatching the fourth qualifying place in the north group and ended Durham’s chances of progress.
Going in when Alex Hales holed out at deep mid-wicket in the third over for three, Wessels drove five leg-side sixes in propelling the Outlaws to 198 for five, to which Durham replied with 156 for six.
Jonny Bairstow last year became the only man to score a T20 century at the Riverside ground and Wessels still had eight balls left to join him when he top-edged an attempted sweep to the wicketkeeper.
The ball was in the air long enough for James Taylor to get to the other end but he spooned the next ball straight to deep backward square.
In making 37 of 22 balls, however, he had helped to put the game beyond Durham in a stand of 98 in eight overs.
Only off-spinner Ryan Pringle commanded any respect, ten of the 24 runs he conceded coming off his fourth over.
Durham’s final home match attracted a crowd of 4,574 for the floodlit encounter and after putting the visitors in they restricted them to ten runs off the first two overs.
But Hales’ departure merely brought in Wessels, who greeted Usman Arshad’s first ball in the fifth over by striking it powerfully through mid-wicket from outside off stump.
The over cost 13 then Wessels drove Chris Rushworth for six as the next over yielded 16 to take the Outlaws to 54 for one after the six powerplay overs.
Wessels cleared long-on twice more in scorching to 50 off 26 balls but a stand of 65 in six overs with Michael Lumb ended when the left-hander chipped to deep cover for 31.
Samit Patel made only four before upper cutting a short ball from Rushworth to be caught by Arshad at third man.
But Taylor followed up his match-winning knock against Lancashire the previous night with another sprightly contribution.
Durham made a spirited start, racing to 39 in 3.4 overs before Phil Mustard lofted a catch to long-on off Dan Christian after making 25 off 14 balls.
Graham Clark then faced three dot balls before giving himself room to drive through the off-side, only to lose his leg stump to Jake Ball.
Paul Collingwood was unable to find the boundary in making 24 off 26 balls before driving Steven Mullany to long-on.
Durham slid to 89 for five in the 14th over, leaving Hastings and Gordon Muchall with an impossible task.
Hastings hit 42 in a stand of 62 before he was bowled off his pads by Harry Gurney’s final ball in the 19th over. Muchall was unbeaten on 30.