Shuck (3-for-5) provided a run-scoring single during the big frame, during which the Angels sent 13 men to the plate, banging out seven hits.
Josh Hamilton went 3-for-5 with three runs scored and an RBI while Mike Trout, Hank Conger and Erick Aybar each drove in two runs for Los Angeles, which pounded out 16 hits overall in the opener of a three-game series.
C.J Wilson (7-5) earned the victory despite allowing five runs on seven hits over five innings, walking two and fanning four.
Detroit's Rick Porcello (4-5) was lit up for seven runs on 10 hits, lasting just 4 1/3 innings.
Notable deaths of 2014 [PHOTOS]
Michael Sam cut from the Dallas Cowboys