The A's walked seven times and reached base on two Tampa Bay errors in their fifth straight win. Starter Tommy Milone (2-3) surrendered two runs on five hits with three strikeouts across 5 2/3 innings to earn the win.
It was the first time since at least 1914 the A's won a regular-season game with just one hit.
James Loney and Yunel Escobar both supplied two hits and an RBI in Tampa Bay's fourth straight defeat. Erik Bedard (2-2) tossed a sold 5 1/3 innings, giving up just one hit and three runs -- one earned -- in the loss.
The two teams will conclude the three-game set on Thursday.