Wells stroked an undefeated 100 and hit the winning runs in what was Otago's highest successful fourth-innings run chase.
He also combined in an undefeated 185-run stand with Neil Broom (89 not out) for the fourth wicket. Earlier, he helped set up the win with five for 74.
He joins some pretty prestigious and perhaps surprising company. Bert Sutcliffe and Ken Rutherford, better known for their deeds with the bat, have both taken five wickets and scored a hundred in one innings.
Jack Crawford was the first Otago player to complete the feat when he scored an undefeated 178 and took five for 149 against Wellington almost 100 years ago.
All-rounder Gren Alabaster also scored 108 and grabbed five for 49 against Central Districts in 1964-65.
Wells was more relieved his side had knocked off the 379 runs required for victory than he was excited about his own effort.
''First of all, it is nice to win and nice to contribute to a win,'' he said.
''To do it with both bat and ball is pleasing.''
Wells has been in good form with the ball this summer but has struggled with the bat. He rectified that with a fine innings under pressure.
''I still see myself primarily as a batsman but I've been in pretty horrific form to be fair, so it has certainly played on my mind.
''I've been looking to make a big contribution with the bat and been working as hard as ever. For whatever reason today it clicked and got us across the line.
''I have not had a chance to hit the winning runs for Otago in my career, so that was an awesome.
''This [win] was massive for us and keeps us in the hunt for the Plunket Shield.
''Last year we fell at the final hurdle in Wellington and that still haunts a lot of us. We want to try and put that right.''
The winning shot was a boundary down the ground. It took Wells to his 100 and Otago to 381 for three. The province's previous-highest successful fourth-innings runs chase was 342 for six against Central District in 1986.
The win has seen Otago consolidate third place on 55 points. Canterbury leads the tournament with 67 points from Wellington (57 points). With four rounds remaining, the title is still wide open.
Otago's terrific run chase was almost ruined by poor weather, though.
The teams spent four hours in the dressing room waiting for the rain to clear yesterday. Wells had plenty of time to think about the 38 runs his side still needed for victory.
Once the teams got back on the park, the end came quickly. Canterbury was guilty of some atrocious bowling.
A series of outrageous wides and ridiculous bouncers which sailed well over the head and down to the boundary were offered up.
Either Canterbury had not warmed up properly or the team was in a hurry to be done with the forlorn cause and wanted to deny Wells and Broom the opportunity to reach a hundred.
Wells was not of the opinion Canterbury let its standard drop to below what you would expect from professionals.
''It was pretty tough for them. We were in the changing room for four hours and it was pretty disorganised when we came out and I don't know if they were warmed up completely or what their plans were.''
On Saturday, Otago opener Hamish Rutherford scored 96 to set a good platform for Otago successful chase.
Otago spinner Mark Craig took eight wickets for the match.
