Verlander, who was pitching on short rest after dominating the Rays in Game 1, was chased in the fourth inning after allowing four earned runs on seven hits. He had five strikeouts and walked three.
The best-of-five series shifts back to Houston for a series-deciding Game 5 on Thursday.
The Rays tagged Verlander for three runs in the first inning to grab a 3-0 lead. Tommy Pham blasted a 408-foot solo home run before an RBI single from Travis d'Arnaud and Joey Wendle's RBI double.
Rays shortstop Willy Adames belted a solo homer in the fourth inning to boost Tampa Bay's advantage to 4-0. Astros catcher Robinson Chirinos scored the team's lone run with a solo shot to right-center field off Colin Poche in the bottom of the eighth.
Ryan Yarbrough, who was credited with the win, and five other pitchers combined to throw a six-hitter for the Rays.
Cy Young Award winner Blake Snell entered the game out of the bullpen for his first career relief appearance and earned the save. Diego Castillo, who started the game for Tampa Bay, pitched 1 2/3 innings and gave up one hit. He struck out three and walked one.