Pujols had two hits and Kendrick went 3-for-4 in support of Jason Vargas (2-3), who earned the victory by holding the Royals to two runs of five hits over seven-plus innings.
Mike Trout and Josh Hamilton chipped in with solo home runs for the Angels, who ended a two-game losing streak.
Los Angeles scored two runs in the fourth and added single runs in each consecutive inning while out-hitting the Royals 12-6.
Billy Butler had two RBI for Kansas City. The Royals lost for the fifth time in five starts.
Jeremy Guthrie (5-1) took the loss for the Royals, ending his streak of unbeaten starts at 18. Guthrie returned to Earth with five runs on 11 hits over seven innings.
Swim Week Miami Beach 2014 [PHOTOS]