The home county, who had won the toss, were eventually bowled out for 534 with Scott Borthwick taking all four wickets to fall after lunch, in taking five for 79.
Durham replied with 75 for one, having lost Keaton Jennings for 26 just before tea.
Nottinghamshire’s seventh wicket partnership was eventually broken after Brett Hutton had added 197 with Wessels, with substitute fielder Graham Clark catching Hutton on the deep midwicket fence.
Jake Ball came and went in a hurry, hitting a four and a towering six in his 10, before he also hit the leg spinner away on the leg side. Graham Onions kept his balance superbly to take the catch inches from the rope.
Jackson Bird chopped on for 11 and Harry Gurney was caught at slip by Paul Collingwood for his fourth nought of the season.
Wessels, who faced 211 balls and hit 20 fours, was left undefeated, having registered his highest score for four years.
Mark Stoneman and Jennings raced out of the blocks, adding 72 for the first wicket but in the penultimate over of the session Jackson Bird claimed his 12th championship wicket of the season, having Jennings caught by Samit Patel at short midwicket.