The Blue Jays were clinging to a 1-0 lead in fourth inning when J.P Arencibia collected a two-out single against Anthony Swarzak (3-6) and Johnson followed by golfing a 3-2 pitch over the right-center field wall.
Rajai Davis and Yunel Escobar each added an RBI single as Toronto clinched its season-ending series.
Jenkins (1-3), a 2009 first-round Toronto draft choice, notched his initial win in his third big-league start, holding the Twins to a pair of runs on five hits over five frames.
Swarzak surrendered four runs on five hits in a five-inning effort.
Denard Span went 2-for-4 with a two-run homer and Ben Revere added three hits for Minnesota.