Shuck's sacrifice fly in the fifth inning put the Angels ahead to stay at 2-1 and Los Angeles put the game away with four runs in the eighth, capped by another Shuck sac fly.
In between, the Angels got RBI from Kole Calhoun and Chris Nelson, clinching their three-game series.
C.J. Wilson (12-6) went 5 1/3 innings to get the decision, allowing two runs on seven hits. He overcame four walks and struck out six.
Indians starter Ubaldo Jimenez (8-7) was saddled with the loss, giving up three runs (two earned) on five hits over 6 1/3 innings.
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