The 30-year old right-hander scored an undefeated 159, making his runs from 211 deliveries, with 20 fours, as Notts totalled 534 before being bowled out after lunch.
Wessels and Brett Hutton, who scored a career best 74, batted throughout the morning session together, before being parted after a stand of 197.
Scott Borthwick took all four Nottinghamshire wickets to fall during the day, to finish with figures of five for 79.
Borthwick then chipped in with an unbeaten half century as Durham responded with 193 for four, still trailing by 341 runs, with all of the wickets falling to Jackson Bird, who has four for 59 so far.
Wessels had earlier reached the 19th first class century of his career from 156 balls and needed only 42 more before reaching the 150 milestone.
Nottinghamshire’s seventh wicket partnership was eventually broken when Hutton lifted Borthwick into the hands of Graham Clark, on as substitiute for the injured Brydon Carse, out 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.
Bird chopped on for 11 and Harry Gurney was caught at slip by Paul Collingwood for his fourth nought of the season.
When Durham batted Mark Stoneman and Keaton Jennings raced out of the blocks, adding 72 for the first wicket but then both fell to Bird, either side of tea, as the Australian took three for none in seven deliveries.
Both openers chipped tamely to Samit Patel at short midwicket and then Jack Burnham was given out lbw first ball.
Michael Richardson lost his off pole to Bird for 17 but an unbroken stand of 72 between Borthwick and Collingwood put the visitors back on track but a further 192 are still required, in order to save the follow on.