The Cardinals, trying to become the first wild-card team in seven years to win baseball's championship, survived a series of dramatic moments and late-inning strategy to slow down the No. 1 hitting team in the majors.
St. Louis Manager Tony La Russa used six pitchers over the final three innings to keep the Rangers at bay after winning pitcher Chris Carpenter had given up two runs on five hits over six frames.
The Cardinals will host Game 2 Thursday. Texas has not lost back-to-back games since Aug. 25.
Craig was called on to bat for Carpenter and he came through with a base hit to right on a 1-2 pitch, bringing in Freese with the final run of the game.
A parade of relief pitchers then headed to the mound, combining to give up one hit and one walk. Both those base runners came in the seventh, but with men on first and second with one away Marc Rzepczynski came on to strike out the only two men he faced on seven pitches to end the last of the Texas threats.
Jason Motte finished off the relief effort with a perfect ninth and his fifth save of the playoffs.
Lance Berkman singled in the first two St. Louis runs in the fourth and Mike Napoli countered with a two-run homer in the fifth for Texas. Napoli, however, grounded into a double play in the second with runners on first and second and one out.
Wilson has lost all three of his decisions in the 2011 playoffs. Carpenter is 3-0, having kept the Cardinals alive by throwing a three-hit shutout in a 1-0 victory over Philadelphia in the deciding game of their NL Division Series.