The Reds (78-73) did move ahead of the Philadelphia Phillies (76-74), who lost 2-0 to the Baltimore Orioles to fall four games behind the Cardinals (80-69).
The Reds are 9-16 in their last 25 games, while the Cardinals are 17-8 in the same span of games.
The Reds have 11 games to play. The Cardinals have 13 games left.
The Cardinals now have a 79.1 percent chance of winning the wild card, according to FanGraphs.com. The Reds have a 14.8 percent chance.
Here’s how their schedules compare:
• Cardinals: Sept. 21-23, at Milwaukee Brewers; Sept. 24-26, at Chicago Cubs (66-83); Sept. 28-30, vs. Milwaukee; Oct. 1-3, vs. Cubs.
• Reds: Sept. 21-22, vs. Pittsburgh Pirates; Sept. 23-26, vs. Washington Nationals; Sept. 28-29, at Chicago White Sox; Oct. 1-3, at Pirates.
The winner of the second wild-card will play on the road against the Giants or Dodgers, whoever doesn’t win the West Division, on Oct. 6. That game will air on TBS.