The Mariners trailed 3-1 entering the seventh, when Dustin Ackley and Ichiro Suzuki drew walks and Munenori Kawasaki singled to load the bases with two outs against Orioles starter Jason Hammel (8-4).
That brought up Wells, who sliced an 0-1 pitch into the right-center field gap, chasing home all three runners.
Ackley and Miguel Olivo homered for Seattle, which took the opener of a three-game series.
The rally made a winner of Steve Delabar (2-1), who tossed two scoreless frames in relief of starter Hisashi Iwakuma. Tom Wilhelmsen collected his seventh save.
Hammel ended up allowing four runs on seven hits in a 6 2/3-inning stint for Baltimore, which fell for the sixth time in seven games.
Chris Davis bashed a three-run homer for the Orioles.
Celebrity Families of 2014 [PHOTOS]