Greinke went five innings Tuesday and gave up one run on seven hits and two walks.
Albert Pujols and Alberto Callaspo also notched RBI for the Angels, who have won four in a row and are two games behind Oakland in the hunt for the final wild card playoff berth.
Justin Smoak had two home runs for the Mariners, including a two-run shot in the seventh that cut the Los Angeles lead to 5-4.
Rookie Erasmo Ramirez (1-3) took the loss on five runs -- three earned -- off seven hits and three strikeouts in six innings.
Celebrity Families of 2014 [PHOTOS]