ALCS MVP Randy Arozarena smashed a two-run homer in the first inning to set a new rookie postseason record with his seventh playoff long ball.
Rays right-hander Charlie Morton carved through the Astros' lineup, allowing two hits over 5 2/3 scoreless innings. He retired 14 straight from the end of the first through the start of the fifth inning and was lifted after throwing 66 pitches (48 strikes).
Morton was credited with the win, which furthered his growing legend in winner-take-all games.
The Astros made it close late by scoring a pair of runs in the eighth inning on Carlos Correa's two-run single, but that was all they mustered.
Astros starter Lance McCullers Jr. allowed three runs on four hits while striking out seven over 3 2/3 innings. In addition to Arozarena's bomb, McCullers served up a towering solo homer to Rays catcher Mike Zunino.
Despite the disappointing finish, McCullers tipped his cap to the Rays.
"It sucks, man," McCullers said, according to Brian T. Smith of the Houston Chronicle. "It really does. But congrats to the Rays. They're a really good team."
Tampa Bay stormed to an early advantage in the series, winning the first three games before dropping three straight to force the decisive contest. With the loss, the Astros failed to become the second team in MLB history to come back from a 3-0 series deficit.
The Rays team that reached the Fall Classic in 2008 split the opening two games against the Philadelphia Phillies before ultimately falling in three straight to lose in five.
Tampa Bay will face the winner of Sunday's Game 7 of the NLCS between the Los Angeles Dodgers and Atlanta Braves. The World Series begins Tuesday, Oct. 20.