With the Twins trailing 4-2 entering their final at-bat, Mariners closer Tom Wilhelmsen (0-1) issued consecutive walks to Pedro Florimon, Eduardo Escobar and Joe Mauer, loading the bases with none out.
Florimon scored on Josh Willingham's sacrifice fly, cutting the Twins' deficit to one run, and Doumit followed by belting a pitch to the wall in right-center field, sending home Escobar and Mauer with the game-winning runs.
Doumit finished 3-for-5 for Minnesota, which evened its three-game series.
Caleb Thielbar (1-0) earned his first major league victory after tossing a 1-2-3 top of the ninth.
Jason Bay launched a pair of solo homers and Kyle Seager added a bases-empty clout for the Mariners.