Trumbo had given the Angels an early 4-0 lead but Minnesota battled back against Jered Weaver (16-7), who earned the victory despite allowing six runs on eight hits over five innings.
With the score tied 6-6 in the fifth, Wells hit a ball off the top of the center field fence that was confirmed as a go-ahead homer after a video review and the Angels went on to even their three-game series with the Twins.
The victory allowed second-place Los Angeles to gain a game on American League West-leading Texas, pulling to within 3 1/2 games.
Phil Dumatrait (1-3) took the loss after yielding Wells' homer after starter Brian Duensing lasted only 1 1/3 frames, in which he surrendered five runs on three hits.
Trevor Plouffe drove in four runs with a bases-clearing double and a run-scoring single for the Twins.