St. Louis has won six of its last seven, including the first two games of this three-game set. The first-place Cardinals have won eight of their last 10 against the third-place Reds and lead them by 4 1/2 games in the NL Central.
The Cards also moved 1 1/2 games ahead of second-place Pittsburgh, which lost to Milwaukee.
Shin-soo Choo homered for Cincinnati, which lost for the fourth time in five games. The Cardinals retired the last 13 Cincinnati batters, dropping the Reds to 4-10 against St. Louis this season.
Kelly (6-3), who allowed one run on nine hits, improved to 6-0 in nine starts since rejoining the starting rotation on July 6. The Cardinals have won the last six games he has started. Kelly began the season in the bullpen.
Holliday, who went 2 for 3, keyed a two-run outburst in the first against Mat Latos (13-5), who gave up four runs on nine hits over six innings. He struck out four and did not walk a batter.
Arizona slugger Paul Goldschmidt had an eight-game RBI streak in early June - a season best in MLB.
The Cardinals needed just 14 pitches to take a 2-0 lead. Matt Carpenter and Carlos Beltran began the opening frame with singles. Holliday followed with a hit to right to bring in Carpenter, who scored his major league-leading 100th run. Allen Craig then hit into a double play, allowing Beltran to score from third.
Choo brought the Reds to 2-1 with a leadoff homer in the fifth, the 100th round-tripper of his career and 17th of the season.
The Cardinals answered with single runs in the sixth and seventh and scored twice in the eighth.
Craig pushed the lead to 3-1 with his team-leading 96th RBI on a run-scoring double in the sixth. Carpenter brought in Jon Jay with a sacrifice fly in the seventh. Jay and Daniel Descalso singled to start the inning.
Notes: Adam Wainwright (15-7, 2.58 ERA) faces Homer Bailey (8-10, 3.71) in the final of the three-game series Wednesday. Bailey is 0-5 with a 6.90 ERA in seven career starts at Busch Stadium. ... St. Louis INF Pete Kozma is mired in a 0-for-23 slump. ... The Cardinals are 34-22 against NL Central opponents this season with 22 divisional games remaining. ... The Reds have spent the past 127 days in second, third or fourth place.
Link to box score: St. Louis 6, Cincinnati 1
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