Sussex resumed on the fourth morning on 237-4, needing 309 for the win with Wells going well on 74 not out alongside Ben Brown, who began on 39 not out.
The pair steered the total to 277 before Brown (61) became the first of four Ruel Braithwaite victims.
Wells was the second, though only after reaching 103, and although Rana Naved-ul-Hasan and Joe Anyon were dismissed in the same over, Amjad Khan and Andy Hodd saw Sussex over the line.
Warwickshire made it two wins from as many matches as Chris Woakes completed a recovery underpinned by Varun Chopra’s batting marathon against Worcestershire at New Road. Although the opener finally departed for a career-best 228 as five wickets fell in 54 balls on the final morning, the visitors were able to declare at 461-8 before rushing the home side to their second defeat.
Set 278 in 75 overs, Worcestershire were quickly put on the rack by Woakes and the England pace prospect had figures of 6-49 when they were dismissed for 199, subsiding to an 88-run defeat with time to spare.
Middlesex continued their impressive start to the Division Two season when half-centuries from Gareth Berg and Ollie Rayner carried them to a thrilling three-wicket victory at Derby.
Derbyshire looked favourites when Middlesex slipped to 197-6 chasing 328, but Berg and Rayner turned the game with a stand of 97 in 24 overs.
Essex’s Matt Walker and Mark Pettini both struck unbeaten half-centuries as Essex secured a draw on the final day of their clash with Northamptonshire.
It had looked the most likely outcome at the start of play and an unbeaten partnership of 147 between Walker and Pettini ensured that was the case as the visitors batted out the day in reaching 229-4.
Gareth Rees and Michael Powell both struck half-centuries as Glamorgan batted out for a draw on the final day of their game against Surrey at Cardiff.
At the start of play Surrey still had hopes of registering a win and were able enforce the follow-on, but Rees and Powell frustrated them for nearly two-and-a-half hours in a third-wicket stand of 129 in 42 overs.
Surrey had to be content with nine points to Glamorgan’s eight.