St. Louis took a 2-1 advantage in the series and could wrap up the league pennant with victories at home Thursday and Friday.
The Brewers closed within a run in the third but the St. Louis bullpen threw four hitless innings without a walk to nail down the victory. The St. Louis relief corps has allowed only four runs over the last 23 2/3 innings of playoff baseball.
St. Louis did all its offensive damage in the first by batting around against Yovani Gallardo, who fell to 1-1 in the playoffs. The first five men reached base and the Cardinals would have had an even bigger inning had not Yadier Molina grounded into a double play as the sixth batter in the frame.
That brought up Pujols, who went 2-for-2 in the game and raised his batting average in this year's playoffs to .452. After his ground-rule double scored Jay, Matt Holliday and Lance Berkman walked to load the bases.
Molina grounded into the double play, allowing Pujols to score, and David Freese then added a double that brought home Holliday with the last run of the inning.
Milwaukee scored twice in the second off Scott Carpenter on an RBI single by Yuniesky Betancourt and a sacrifice fly from Gallardo. Mark Kotsay hit a solo homer in the third, but the St. Louis bullpen was soon in action.
Fernando Salas, Lance Lynn, Marc Rzepczynski and Jason Motte all threw an inning of relief for the Cardinals. Motte picked up his third save in as many chances during the playoffs, having allowed one hit in six innings.