Los Angeles won its sixth straight contest, but the Angels are still six games below the breakeven mark.
Chris Iannetta hit a solo homer in the sixth to lift the Angels into a 2-2 tie and they then moved in front with a big seventh inning.
After Trout and Albert Pujols walked to start the inning, Trumbo's single delivered the run that put Los Angeles in front for good. A sacrifice fly by Howie Kendrick and a double by Alberto Callaspo accounted for the other two runs in the inning.
The comeback made a winner out of Jason Vargas (4-3), who held Kansas City to two runs on five hits in 7 1/3 innings. Garrett Richards recorded the final five outs to earn his first save.
Kansas City reliever Luke Hochevar was charged with the go-ahead run in the seventh. The Royals lost their third in a row.