Trumbo, who had hit just .177 with 62 strikeouts in his previous 37 games to drop his average from .306 to .268, homered off Will Smith (5-8) in the second inning.
Haren (11-11) improved to 3-1 in his past four starts, holding the Royals to three runs, two earned, and five hits, while walking one and striking out five. He also moved to 4-0 in five career starts at Kansas City.
Torii Hunter, who has 17 RBIs in his past 18 games, singled home Erick Aybar, who had doubled, in the first inning.
After Haren departed, the Royals managed just one hit off Angels relievers Nick Maronde, Garrett Richards, Scott Downs, Jordan Walden and Kevin Jespen.
After closer Ernesto Frieri gave up two home runs in the ninth Saturday to blow a save and take the loss, Jespen was summoned in the ninth and picked up his second save in four chances. Jespen has held opponents to one earned run in 11 2-3 innings in his last 12 outings.
The Angels got a major scare in the fourth inning when outfielders Mike Trout and Hunter collided while chasing Billy Butler’s double to right-center. Manager Mike Scioscia and the trainer came out, but both remained in the game. Butler wound up scoring on Howie Kendrick’s throwing error after Jeff Francoeur’s infield single, trimming the Angels’ lead to 4-3.
Tony Abreu led off the Kansas City third with his first home run in nearly two years. Abreu’s previous home run was Sept. 26, 2010, while with Arizona against the Los Angeles Dodgers.
Salvador Perez, who had the walk-off homer Saturday, doubled to lead off the second, advanced to third on Mike Moustakas’ ground out and scored on Jeff Francoeur’s ground out for the Royals’ first run.
Smith gave up four runs on seven hits and two walks in five innings.