Rick Porcello (5-10) allowed eight hits and three runs -- two earned -- over six innings for the win.
Trevor Bell (1-3) was tagged in the loss for nine hits and six runs -- four earned -- over 5 1/3 frames.
The Tigers moved ahead with three runs in the home sixth. Jhonny Peralta singled with one out, then Ryan Raburn followed with a hit and Brandon Inge walked to load the bases. Avila then slugged the go-ahead two-run single before Bell was yanked for Michael Kohn. Two batters later, Rhymes added an RBI single for a 6-3 game.
Abreu's groundout in the seventh made it a two-run game, but Detroit extended its lead in the eighth on Damon's two-run single and an RBI hit by Austin Jackson.
Jose Valverde worked around a walk in the ninth and closed out the game with a scoreless frame.
Detroit tallied three times in the fifth on a run-scoring single by Don Kelly and back-to-back doubles from Rhymes and Damon, but LA came back with two in the sixth on RBI hits from Rivera and Mathis.
Detroit won six of the 10 meetings over Los Angeles this season, including four of six at Comerica...Bell is the grandson of Bob Bell, who was the original Bozo The Clown...Raburn finished with two hits and scored twice...Izturis, Rivera and Reggie Willits added two hits for the Angels...The Tigers stay home to face Tampa Bay and the Angels head home to host Kansas City on Monday.