Freese hit a two-run triple just over a leaping Nelson Cruz to tie the score 7-7 in the ninth inning against Neftali Feliz. Then, after Josh Hamilton put Texas ahead with a two-run homer in the 10th off Jason Motte, Ryan Theriot hit an RBI groundout in the bottom half and Lance Berkman tied it 9-9 with a single.
Freese's shot to center came off Mark Lowe.
Game 7 is Friday night.
Texas had built a 7-4 lead in the seventh when Adrian Beltre and Nelson Cruz hit consecutive home runs off Lance Lynn, and Ian Kinsler added an RBI single off Octavio Dotel.
Allen Craig's second homer of the Series cut the gap in the eighth against Derek Holland.
In the ninth, Albert Pujols doubled with one out off 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, sending the game to extra innings.
With Texas ahead 3-2 in the Series and one win from its first title, the Rangers also 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, with each team allowing two unearned runs.
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 Alexi Ogando.
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.
Texas went ahead 10 pitches in. After starting with a called strike, Garcia walked Kinsler on four straight pitches, and Elvis Andrus' hit-and-run single put runners at the corners. Hamilton pulled the next pitch into right field for a single and his third RBI of the Series.
Garcia recovered to strike out Young and Beltre, then got Cruz to hit into an inning-ending forceout on his 23rd pitch.
Lewis quickly gave back the lead. Skip Schumaker, moved up from eighth in the batting order to second, singled with one out in the bottom half. Pujols flied out on the next pitch. Berkman also swung at the first pitch, sending an 89 mph offering over the center-field wall.
Napoli walked leading off the second and Gentry singled him to second. Lewis bunted directly at Freese, who started a rare 5-6-4 double play. Shortstop Rafael Furcal took the throw at third for the force, then threw to second baseman Nick Punto covering first.
Kinsler followed with a ground-rule double that hopped over the left-field fence, tying the score 2-all. La Russa then had Mitchell Boggs start warming up after Garcia had thrown just 42 pitches to 10 batters,
Andrus hit an inning-ending lineout to right that Berkman slightly misjudged and caught with a jump.
Schumaker and Pujols flied out just in front of the warning track in the third. Other than his 5-for-6, three-homer, six-RBI performance in Game 3, Pujols is 1 for 17.
St. Louis, tied for fourth in the majors in errors during the regular season, started to get sloppy in the fourth. Cruz led off with a fly to short left, where Holliday called for Furcal to take it, only for the shortstop to back off. The ball then bounced off Holliday's glove for a two-base error.
Napoli sliced a single down the right-field line, kicking up chalk from the foul line, to put Texas ahead 3-2. After Gentry struck out, Lewis bunted to Pujols, who threw to second in time for a forceout, but first base umpire Jerry Layne called the ball foul. Lewis bunted the next pitch to Salas, who threw the ball into center field. Not sure whether to slide, Napoli went in awkwardly and turned his left ankle. He stayed in, but the base was later replaced.
Salas escaped further trouble by throwing a called third strike past Kinsler and retiring Andrus on a fly to left that turned Holliday around in the wind.
Berkman led off with a grounder to Young, who bobbled it and made a throw that pulled Lewis off the base for an error on the first baseman. Holliday walked for the second time, and Furcal bounced into a forceout to second, with Andrus' throw to first for a double play way high and bouncing off a screen near the dugout. Molina followed with a grounder to third that drove in his sixth run of the Series.
After Young's double, Napoli was intentionally walked with two outs, and pinch-hitter David Murphy walked to load the bases. While Yorvit Torrealba was in the on-deck circle to hit, Washington left Lewis in the game, and he struck out in three pitches.
Berkman reached on an infield hit. Young then picked up Holliday's grounder, thought about throwing to second and allowed the ball to pop free. Berkman then just beat him to the bag.
Walks to Freese and Molina forced in a run, and Napoli picked off Holliday at third, with Holliday bruising his right pinkie and leaving the game. After a wild pitch, Punto walked and Holland retired Jon Jay on a comebacker.