Rays outfielder Kevin Kiermaier blasted a go-ahead, three-run home run in the second inning that put Tampa Bay ahead for the remainder of the game, while starting pitcher Charlie Morton had another masterful postseason performance to pace the team.
Morton allowed one run and three hits while striking out nine over five innings. The 35-year-old right-hander has a 4-0 record and 0.95 ERA in four career playoff elimination starts, including last week's wild-card win against the Oakland A's.
The Astros jumped out to a 1-0 lead after a solo home run by Jose Altuve in the first. Kiermaier's three-run shot put the Rays ahead 3-1 before Ji-Man Choi and Brandon Lowe added solo home runs off Greinke, who has never won in Tampa Bay, in the next two innings to make it 5-1.
Austin Meadows plated two more with a double in the bottom of the fourth. Rays designated hitter Tommy Pham then scored Meadows with a single to right field, extending Tampa Bay's lead to 8-1.
Greinke was pulled after 61 pitches. He allowed six earned runs on five hits and struck out five across 3 2/3 innings.
Astros first baseman Yuli Gurriel trimmed the lead to 8-3 with a two-RBI single in the sixth. Rays shortstop Willy Adames answered with a solo home run in the bottom of the sixth and Travis d'Arnaud scored Avisail Garcia on a sacrifice fly in the seventh to seal the win.
Game 4 of the best-of-five series is scheduled for Tuesday at Tropicana Field. The Astros will send Justin Verlander to the mound against Rays opener Diego Castillo.