Molina had three hits, including a three-run double, and the Cardinals beat the slumping Atlanta Braves 6-3 on Sunday to complete a three-game series sweep.
The Cardinals pulled within 4½ games of NL wild card-leading Atlanta and remained six games back of Central-leading Milwaukee They have 16 games left and open a three-game set in Pittsburgh on Monday.
The Braves start a three-game series with the Marlins on Monday and have 15 games remaining.
"I feel like we are (in the race) if we keep winning," St. Louis manager Tony La Russa said. "It's exciting baseball. Guys have come through all over the roster. We got a shot."
The Cardinals know they have left themselves no margin for error.
"It doesn't mean anything if you go and you don't have a good road trip," first baseman Albert Pujols said. "We're just going to continue playing and at the end of the road trip we'll see where we are."
Atlanta has dropped seven straight games at Busch Stadium and hasn't won in St. Louis since Sept. 13, 2009. The Braves lost six of eight on their road trip.
"We did nothing right," Braves star Chipper Jones said of the road stint.
"It was a good win for us," Westbrook said. "I would have liked to have gotten deeper in the game and saved our bullpen a little bit but that just wasn't the case."
St. Louis got to Tim Hudson (14-10) for five runs in the third, taking advantage of a lapse in control by the right-hander. Hudson plunked Daniel Descalso leading off the inning, and hit Jon Jay with another pitch with two down, leaving runners on the corners.
Hudson was charged with six runs and eight hits in six innings.
"I made my bed," Hudson said. "I set them up for an inning and I just didn't make good pitches. They had good at-bats and made me pay for it."
Jones did hit a solo drive in the eighth for his 17th homer of the season and No. 453 for his career, moving him ahead of Carl Yastrzemski and into 33rd place. Freddie Freeman singled in a run for Atlanta, and pinch-hitter Matt Diaz had a sacrifice fly.
Braves manager Fredi Gonzalez said his team needs to regroup a bit after playing eight road games in seven days.
"It feels like we're close offensively," Gonzalez said. "Let's just go home, lick our wounds a little bit and go get them."
Cardinals starter Kyle Lohse (13-8) will oppose Brad Lincoln (1-2) on Monday in Pittsburgh. Brandon Beachy (7-2) will get the ball for the Braves on Monday in Atlanta. Chris Volstad (5-12) is scheduled to pitch for the Marlins. ... Freeman's RBI was his 71st, tops among all rookies. ... Pujols went 13 for 36 on the Cardinals' nine-game homestand to raise his average to .297.