Trout's slam capped a nine-run first inning, during which the Angels sent 14 men to the plate, banging out 10 hits.
Peter Bourjos went 3-for-4 with an RBI and two runs scored. Howie Kendrick drove in two runs.
Los Angeles, which clinched its three-game home series, outscored the Tigers 18-1 in the series' first two contests.
Richards (1-0) baffled Detroit on two hits and didn't allow a walk while striking out eight.
Tigers starter Rick Porcello (0-2) was charged with all nine first-inning runs, managing to record just two outs. The right-hander's ERA ballooned to 11.08.