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.