The Cardinals took a 3-2 lead in the National League Championship Series and are one win away from their third World Series appearance in eight years. Milwaukee will host Game 6 Sunday and, if needed, a seventh and deciding game Monday.
St. Louis took advantage of two fielding lapses in the second to take control and the Cardinals' bullpen came through with a two-hit effort over the final 4 1/3 innings.
Molina was next and he hit a 1-1 offering deep to right. Milwaukee's Corey Hart got a glove on the ball but was unable to make the play and both runners scored on what was ruled a double.
Nick Punto followed by lining out to third for what would have been the final out of the inning if Hart had been able to corral the drive by Molina.
St. Louis inched further in front with single runs in the fourth and sixth innings. Holliday closed out the scoring with a two-run double in the eighth.
Garcia did not last long enough to be credited with the victory, giving up a run on seven hits in 4 2/3.
Octavio Dotel recorded the final out in the fifth with two runners aboard and then worked a perfect sixth.
Lance Lynn benefited from a double play while pitching the seventh for St. Louis, then gave up two hits in the eighth before being relieved by Jason Motte with two on and two away.
Motte completed the outstanding relief effort with a perfect ninth. Dotel, who struck out two of the four men he faced, picked up his second win of the playoffs.