Swansea maintained their momentum under Carlos Carvalhal as Ki Sung-yueng's late strike secured a 1-0 home victory over Burnley.
A Premier League game of few chances sprang into life when Ki drilled home low from the edge of the penalty area after 82 minutes -- the midfielder's first goal since May 2016.
Wells had just entered the game as a substitute in the 81st minute.
Swansea have now taken 14 points from 21 since Carvalhal succeeded Paul Clement, climbing from the bottom of the Premier League into 15th place.
Burnley, as resilient and combative as ever, had knocked Swansea out of their stride for much of a dour contest.
But they were left to reflect on another disappointing afternoon, with the longest winless run in the top flight stretching to 10 games.
Reggie Lambe and his Carlisle United teammates played host to Colchester United at Brunton Park.
And it was honors even as Carlisle equalized late in the day courtesy of a stunning free kick from the in-form Jamie Devitt.
Colchester took the lead in the 44th minute when they broke quickly from a corner. Kurtis Guthrie suddenly found himself with just Jack Bonham to beat, as Courtney Senior played him clean through, and it was Senior who was on hand to roll the block from the stopper into the waiting net as the rebound fell at his feet.