Matt Holliday launched his third home run of the season, a two-run blast, in the first inning to give the Cardinals their first lead of the series.
"Holliday's home run meant a lot and did get something positive going, but it's not something we're talking about as a club, [like], 'Hey we've got to score first in order to have a chance for this game,'" Cardinals manager Mike Matheny said. "That's not the train of thought, that's not the conversations we have. Just keep grinding out the game."
Yadier Molina led off the second inning with a double and scored on a wild pitch. Pitcher Carlos Martinez then helped his own cause by slapping an RBI single to right, scoring Kolten Wong to make it 4-0.
"It feels pretty good because I was able to help my team," Martinez said through an interpreter. "I was able to help myself. It feels good because I'm still hitting good and everybody thinks I can hit now."
Molina capped off a 2-for-3 day with an RBI single in the eighth inning.
"He's swinging the bat well, seeing it well," Matheny said. "I thought he was doing a nice job all the way across the board, with what he's doing behind the plate and just looks strong at the plate. It's nice to see him that way."
Before the uprising, the Cardinals were 0-for-their-previous-19 with runners in scoring position. They went 4-for-9 on Wednesday.
One day after a costly baserunning mistake aided a one-run loss, the Cardinals were aggressive and smart on the bases.
Wong stole third in the second inning ahead of Martinez's hit. Wong's second steal of the season moved him into a tie for the team lead with Jeremy Hazelbaker, and it was just the sixth total steal for the Cardinals.
Wong continued the strong baserunning by going first to third on Aledmys Diaz's hit-and-run single to right in the fourth.
Seven of the Cardinals' starting nine got at least one hit.
Counting the playoffs, the win snapped a five-game losing streak to the Cubs.
Joe Harris is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.