Pomeranz (4-1) gave up three hits and two walks with three strikeouts in five innings for the Athletics, who have won four straight and 10 of their last 11. Dan Otero tossed two frames, with Luke Gregerson and Sean Doolittle each pitching one.
Jake Odorizzi (2-4) gave up three runs on four hits with five walks and eight strikeouts in 4 2/3 innings for the Rays, who have dropped their past three games.
The Athletics stranded men on first and third in the first inning, but went ahead in the second.
With one out, Derek Norris walked and Eric Sogard singled two batters later. Crisp then doubled in both runners, and Jaso followed with a single to left for a 3-0 lead.
Tampa loaded the bases with one out in the third, but Desmond Jennings hit into a 6-4-3 double play to end the frame. The play was reviewed to see if Jennings beat the throw to first, but the call on the field was upheld.
The Rays didn't threaten again until the eighth when the team put runners at the corners with one out, but it was Jennings again grounding into a double play, this one a 5-4-3, as the team came away empty.
Doolittle kept the Rays off the board in the ninth for his third save of the season.