"We're gonna come out [tonight] with the same attitude and play great baseball," said the Cardinals' Lance Berkman, who was 3-for-5 with three RBI and four runs scored.
In the top of the 10th inning, Josh Hamilton hit a two-run homer to put the Rangers ahead, 9-7. The Cardinals, however, answered in the bottom of the inning.
Ryan Theriot's groundout allowed Daniel Descalso to score from third and pulled the Rangers to within one run. Scott Feldman, the Rangers' seventh pitcher of the game, then intentionally walked Albert Pujols to get to Berkman. All Berkman did was single to score John Jay from second and move Pujols to third. Feldman then got Allen Craig to ground out and send the game into the 11th.
Adrian Beltre and Nelson Cruz hit consecutive home runs off Lance Lynn, and Ian Kinsler added an RBI single off Octavio Dotel as Texas built a 7-4 lead in the seventh.
Craig's second homer of the Series cut the gap to 7-5 in the eighth.
Then in the ninth, Pujols doubled with one out off Neftali Feliz and Berkman walked on four pitches.
Craig took a called third strike, and Freese fell behind in the count 1-2. He sliced an opposite-field drive, and when Cruz jumped, the crowd of 47,315 at Busch Stadium couldn't tell at first whether he caught it.
Feliz then retired Yadier Molina on a flyout to right, to send the game to extra innings.
In the sixth, Texas reliever Alexi Ogando forced in a run with a bases-loaded walk to Molina, leaving the Cardinals and Rangers 4-4.
The Rangers wasted 1-0, 3-2 and 4-3 leads. The Cardinals made three errors in a Series game for the first time since 1943, and Rangers first baseman Michael Young made two.
Matt Holliday was picked off in the sixth at third base by catcher Mike Napoli, thwarting the Cardinals' attempt to go ahead, and he had to leave the game because of a bruised right pinkie.
Hamilton's RBI single had put the Rangers ahead in the first off Jaime Garcia, Berkman's two-run homer gave the Cardinals the lead in the bottom half and Kinsler's run-scoring double tied it 2-all in the third.
Cruz reached when Holliday dropped a flyball leading off the fourth and came home when Napoli singled for his 10th RBI of the Series. Berkman then got to first on a throwing error by Young starting the bottom half and scored on Molina's grounder.
Freese dropped Hamilton's popup to third leading off the fifth, and Young lined a pitch from Fernando Salas to the gap in left-center. An error by Young on Holliday's sixth-inning grounder was followed by three straight walks, including two by Ogando.
Starter Colby Lewis allowed four runs - two earned - and three hits in 5 1/3 innings.
Texas got far better swings against Garcia than it did in Game 2, when he allowed three hits in six shutout innings. This time, he gave up five hits and two walks, throwing 59 pitches, and seven of the first 13 Texas batters reached base.
Just 24 of the 61 previous teams with 3-2 leads won Game 6, but 41 of those 61 teams went on to win the title. Eighteen teams trailing 3-2 in the best-of-seven format bounced back for championships, including 12 that swept the last two games at home.
In an effort to provide more production behind Pujols, Cardinals manager Tony La Russa moved Berkman to cleanup and dropped slumping Holliday down to fifth.
Rangers manager Ron Washington moved the hot-hitting Napoli up one spot to seventh and had Craig Gentry hitting eighth, as he did in Game 2.
Four Cardinals Hall of Famers, wearing cardinal red sports jackets, stood at home plate before the game. Red Schoendienst, Lou Brock, Bob Gibson and Ozzie Smith. And then the greatest Cardinals player, 90-year-old Stan Musial, was driven from the right-field corner to the plate in a golf cart. Wearing a red sweater and Cardinals warmup jacket, he greeted his fellow Hall of Famers and watched 2006 Series MVP David Eckstein throw out the ceremonial first pitch.