Their lineup likely is in for a tough challenge to continue that surge in the coming days.
St. Louis will face each of the three pitchers who have thrown no-hitters this season over its next five games beginning Thursday night, when Wainwright opposes Los Angeles Dodgers starter Josh Beckett at Chavez Ravine.
"Overall, just a great, gutsy win," manager Mike Matheny said. "To be able to get guys on third with less than two outs and to get the run in, that's who we have to be."
The Cardinals' offense will have its work cut out for it as their road trip hits California, starting with this matchup that marks the first meeting since St. Louis beat Los Angeles in six games in last season's NL championship series.
Beckett (5-4, 2.28 ERA) threw this season's first no-hitter May 25 against Philadelphia. Clayton Kershaw, who struck out 15 Rockies in his no-hitter June 18, will take the mound in the finale of this four-game set Sunday.
The Cardinals begin a three-game series against San Francisco on Tuesday, with Tim Lincecum making his first start since no-hitting San Diego on Wednesday.
The first obstacle is Beckett, who is 3-3 with a 1.58 ERA over his last six starts after striking out eight in seven scoreless innings of Saturday's 4-1 win over the Padres.
"If I get seven (innings) and 100 pitches, that's a pretty successful night," Beckett said. "At this point in my career, I'm not a complete-game guy. My stuff is not as good. I try to battle with what I have and get through six or seven innings."
Wainwright (10-3, 2.08) has pitched through at least six innings in 13 of his 15 outings after giving up one run over eight in Saturday's 4-1 win over Philadelphia.
The right-hander's solid performance came after he was forced to miss a start due to elbow tendinitis. His ERA is second in the majors behind Cincinnati starter Johnny Cueto's 1.86 mark.
"Unbelievable," Matheny said. "This guy has just been so good. Taking a little break and coming back as sharp as he is, I don't know why I'm surprised. To be as sharp as he is with a little time off, he looked like the Adam we've watched all season."
Wainwright is 4-4 with a 2.18 ERA in his last 11 starts - including the postseason - against the Dodgers (44-36), who have won seven of nine after beating Kansas City 5-4 on Wednesday.
A.J. Ellis was hit by a pitch with the bases loaded in the eighth to bring in the deciding run, while Dee Gordon had four hits after going 4 for 23 over his previous seven - and also stole his 40th base.
''Our guys hung in there,'' manager Don Mattingly said. ''We got behind. We threw some runs up there. They came back and we kept playing.''
Yasiel Puig had two hits after going 1 for 14 over his previous four contests. He hit just .227 in the NLCS against the Cardinals, but went 5 for 9 at Dodger Stadium.