The Rays lost their second in a row after winning five straight and remained four games behind Boston in the race for the American League wild-card berth. The Los Angeles Angels trail the Red Sox by 4 1/2.
Vladimir Guerrero then reached on an infield single with one out in the bottom half of the fourth and moved to third on a double by Matt Wieters. Davis followed with a homer to left off losing pitcher Wade Davis (10-9).
Wieters added his third homer in as many games, a two-run blast in the eighth.
Jeremy Guthrie (8-17) equaled a career best with 10 strikeouts and gave up two runs on three hits in seven innings for the victory.