Holliday drove in the winning run with two outs in the ninth inning, and the St. Louis Cardinals rallied from a four-run deficit to beat Los Angeles 5-4 and finish a four-game sweep.
"I've had a chance to face him quite a bit without too much success," said Holliday, who is 4 for 17 against Broxton, many of those at-bats coming with the Colorado Rockies. "He's one of the best closers in the game for a reason."
Pujols got a day off from the starting lineup for only the second time this season.
"It's awesome," Craig said. "It's the best birthday present I ever had."
Craig put the Cardinals on the board with a two-run double off reliever Justin Miller in the eighth that made it 4-2, and he singled to center off Broxton (3-1) with two outs in the ninth to knot the game. Holliday followed with an RBI single over Andre Ethier's head in right field, bringing home Jon Jay with the winning run.
Ryan Franklin (4-1) pitched the ninth for the victory as the Cardinals completed their first four-game sweep of Los Angeles since taking consecutive doubleheaders July 7-8, 1987.
The win also edged the Cardinals (51-41) ahead of the Cincinnati Reds in the NL Central, although it was a different number that caught the eye of manager Tony La Russa.
"The most significant thing is that we're 10 games over .500," he said.
Broxton entered the game with one out in the eighth inning and threw 44 pitches while blowing his third save in 22 chances. It was his first loss since Sept. 27 at Pittsburgh.
"I got myself into bad counts and walked guys," said Broxton, who got Holliday to fly out in the eighth before getting burned in the ninth. "I shouldn't have gotten back around to him."
Garret Anderson had a pinch-hit RBI double and Matt Kemp brought home a run with a walk for Los Angeles, which wasted a superb effort by Vicente Padilla. He allowed only one hit while pitching six scoreless innings.
The Dodgers took their first lead of the four-game series in the fifth inning against St. Louis starter Jeff Suppan. With one out and runners on first and third, Padilla chopped a ball over the head of third baseman Felipe Lopez and into the corner in left to score Xavier Paul.
Los Angeles added three more runs off reliever Mitchell Boggs in the seventh, but the Cardinals closed to 4-2 in the eighth on Craig's double to left with one out off reliever Justin Miller. Broxton came on and allowed Randy Winn's RBI single before getting out of the inning.
"It was tough, very tough," said Los Angeles manager Joe Torre. "We just asked too much out of Brox. You certainly don't want a closer to come in and face the same guy twice. It was a tough one to let get away."
Dodgers 1B James Loney, who was helped off the field in the ninth inning with cramps Saturday, was held out of the starting lineup. ... Dodgers manager Joe Torre, a former Cardinals player and manager, received a standing ovation prior to the sixth inning when his birthday was announced. He tipped his cap from the top step of the dugout. ... Padilla was 1 for 13 before his RBI double.