Palmer led off the second inning with a home run on an 0-2 pitch, then hit his team-record sixth career grand slam an inning later. He has four homers this year, all in the last four games.
Greer homered in the first, singled ahead of Palmer's grand slam and singled again in the fifth, scoring on a single by Lee Stevens that chased Guzman (2-2). Greer's three hits upped his career average against Guzman to .600.
Rodriguez's homer, his first of the year, came on the first pitch of the fifth inning. He also singled home a run in the eighth.
This was the second consecutive bad outing for Guzman, and the first time in his career he gave up four homers. He gave up nine runs on 10 hits with three walks and two strikeouts in 4 1/3 innings.
His earned-run average more than doubled, from 2.84 to 5.79. It shouldn't have been much of a surprise--despite an AL-best 2.93 ERA last year, Guzman had a 7.41 ERA against Texas, losing all three starts.
His ERA against the Angels last season was 3.60.
Ed Sprague, who entered the game with a major league best nine doubles, had another one in the sixth for the Blue Jays.
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NEXT SERIES FOR ANGELS
WHO: Toronto Blue Jays
WHERE: Anaheim Stadium
WHEN: Monday 7 p.m., Tuesday 7 p.m. and Wednesday 7:30 p.m.