Josh Hamilton and Michael Young drove in the runs in the ninth with sacrifice flies, turning what appeared likely to be a two-game lead for the Cardinals into an even series heading back to Texas, where the Rangers will host the next three games, beginning Saturday with Game 3.
Texas, which avoided what would have been its first two-game losing streak in almost two months, managed only three hits through the first eight innings and was facing Jason Motte in the ninth.
Motte had five playoff saves this season in five opportunities and was working in chilled weather that had helped silenced the Texas bats.
Kinsler, however, reached on an infield single to open the ninth and stole second while Andrus was at the plate. Kinsler's hand barely reached the second base bag ahead of the throw from catcher Yadier Molina.
Andrus then singled to center with Kinsler holding at third and when the throw back to the infield slipped past the cutoff man Andrus dashed to second.
St. Louis Manager Tony La Russa, praised for his handling of the St. Louis bullpen in the 3-2 St. Louis win to open the series, then lifted Motte for Arthur Rhodes. Hamilton hit the first pitch from Rhodes to medium deep right field and Kinsler easily scored the tying run.
Andrus moved to third on the Hamilton fly ball and scored with ease when Young lifted a fly ball to right off Lance Lynn, who had come in to replace Rhodes.
The win went to Mike Adams, who stranded two runners in the eighth during his only inning of work. St. Louis left nine runners on base overall.
Until the Texas comeback, Allen Craig had put himself in position to be a hero for the second straight night. Craig, who drove in the game-winning run in the series opener, singled in the only Cardinals' run in Game 2.
Thursday's game was played in temperatures that dropped through the 40s -- heading toward the likelihood of overnight frost in the St. Louis area. Temperatures are forecast to be in the 80s in Arlington during the weekend despite the chance of rain.
Hamilton and Young, who drove in the runs in the ninth, were a combined 1-for-14 in the first two games of the series. St. Louis star Albert Pujols is 0-for-5 with a run scored.