The Rays' offense did just enough to win, as Evan Longoria hit an RBI double in the fourth, Rocco Baldelli drove in a run in the fifth and Willy Aybar hit a solo home run in the seventh.
Rookie pitcher David Price was the late-inning hero, pitching the final 1 1/3 innings to get the save and preserve a 3-1 win to send the Rays to their first World Series.
"I knew we were going to be good, but never in a million years would I ever have expected this," Rays lefty Scott Kazmir said afterwards. "I don't think anyone did, until we got halfway done with the season. After that, we knew; we knew we had something."
Every day from now to Spring Training, MLB.com/Live will air a classic game on Baseball's Best
. The Rays' clinching win can be seen on Thursday at 3 p.m. ET.
It was an amazing win for the Rays, especially after what they had gone through in Games 5 and 6. After all, they held a 7-0 lead in the seventh inning against the Red Sox in Game 5 and lost a heartbreaker in Game 6 to send the series to the final game.
But Tampa Bay proved it still had some fight left and Garza simply would not let the Rays lose. Garza, who also shut down the Red Sox in Game 3, pitched superbly to garner ALCS Most Valuable Player Award for his efforts.
"In the biggest stage of his life," Rays pitching coach Jim Hickey said at the time, "he came up with one of the biggest games of his life."
Tampa Bay's offense also did its job against Boston starter Jon Lester, who allowed three runs on six hits over seven innings.
The Rays tied the game in the fourth inning when Akinori Iwamura singled to open the frame and scored on a double by Longoria, who had eight RBIs in the series.
And Tampa Bay took the lead in the fifth when Aybar doubled to open the inning and reached third on a single by Dioner Navarro before Baldelli drove home Aybar on a single to left field.
The Rays then added an insurance run in the seventh on a solo blast by Aybar to go up 3-1, which was more than enough for the Tampa Bay bullpen.
But the bullpen had a few scares when manager Joe Maddon used Dan Wheeler, Jay Howell, Chad Bradford and Price over the last two innings.
In the end, however, Price was the hero. The rookie left-hander did not allow a hit over 1 1/3 innings and struck out three of the five batters he faced.
He got Jed Lowrie to ground out to second base for the last out of the game to give the Rays their first American League pennant.
The trip to the World Series surprised just about everybody in baseball except the Rays, who played the game as if it were any other game.
"Today was us when we came in," Cliff Floyd said after the game. "It was how we played all season. It was how we prepared ourselves. BP was the same, nobody stretched, we messed around -- that's what we did all season. There's really nothing else to say except nobody would have thought this in a million years."