Rogers' multi-homer game gave him 19 for the season.
Matt Vierling supplied two hits and scored a run, while Kerry Carpenter knocked in the other run for Detroit (70-79).
Miguel Diaz pitched one scoreless inning to start the game. Winning pitcher Joey Wentz (3-11) tossed 4 1/3 innings, giving up three runs and five hits while striking out seven. Alex Lange got the last three outs for his 24th save as the Tigers won their fourth straight.
Randal Grichuk hit a two-run homer for the Angles (68-82). Losing pitcher Kenny Rosenberg (1-2) allowed all five runs on seven hits in five innings.
Rogers' first long ball of the game came off Rosenberg in the second inning and cleared the left field wall.
Rosenberg gave up four more runs the next inning. Parker Meadows walked, Vierling singled and Andy Ibanez walked.
After Spencer Torkelson popped out, Meadows scored on Carpenter's groundout. Rogers then drilled a fastball over the right center wall to make it 5-0.
The Angels had runners in scoring position in the fourth but Wentz retired Eduardo Escobar on a grounder to end the threat.
The Tigers had runners on the corners with two out in the fifth but this time Rogers couldn't deliver as he bounced into a fielder's choice.
Nolan Schanuel doubled with two out in the bottom of the inning for Los Angeles and Fletcher knocked him in with a single.
The Angels pulled within 5-3 in the sixth. Logan O'Hoppe drilled a one-out single before Grichuk's 15th homer over the left field wall off Wentz.
Lange gave away a three-run lead in the ninth on Saturday night. On Sunday, he retired Escobar on the fly ball, then struck out Brett Phillips — who hit a game-tying homer off him the night before — looking. Zach Neto lined out to end the game.
—Field Level Media