The Angels were trailing 3-1 when Hank Conger led off the seventh with a single against Mike Gonzalez.
That brought up Shuck, who sent a sharp grounder down the first base line that glanced off the glove of Yuniesky Betancourt for a three-run double.
Kole Calhoun went 2-for-4 with two RBI and Mike Trout added three hits for Los Angeles.
C.J. Wilson (14-6) yielded three runs on three hits over six innings for the victory, walking two and striking out three.
Ernesto Frieri finished up the win with his 30th save.
Carlos Gomez cracked a two-run homer for the Brewers.
Celebrity Couples of 2014 [PHOTOS]