CINCINNATI — After winning 14 games in both 2005 and 2006, Bronson Arroyo naturally wanted to do better.

It took him a season longer than he expected, but the Reds right-hander did it Tuesday night with two starts to spare. Arroyo improved to 5-0 in his last six starts and Edwin Encarnacion hit a three-run double to lift the Cincinnati Reds to a 7-2 win over the reeling St. Louis Cardinals.

‘‘It was nice getting that 15th win and getting over that plateau — and I still have two starts left,’’ said Arroyo, who slipped to 9-15 last season after winning 14 games for Boston in 2005 and the Reds in 2006. ‘‘It’s nice to have a little breathing room.’’

‘‘Fifteen — that’s huge,’’ manager Dusty Baker said. ‘‘Let’s go for 16. Heck, he’s got a chance for 17. Let’s run the table.’’

Arroyo (15-10), who had allowed just two homers in his previous eight starts, gave up two in seven innings, but he still lasted long enough to help send the Cardinals to their season-high sixth consecutive loss.

‘‘Right now, we’re not getting all the phases of the game,’’ said St. Louis starting pitcher Braden Looper, who went into the game with a 4-1 record and 2.93 ERA in 34 appearances — including four starts — against the Reds. ‘‘If we score seven runs, we give up eight. If we hold them to two, we only score one.’’

Arroyo allowed five hits with no walks and four strikeouts.

Looper went seven innings while setting single-season career highs with his 31st start and 13th loss. Looper (12-13) allowed six hits and four runs. He also hit a batter.

‘‘This was the kind of game where both pitchers were sharp and you couldn’t afford to make a mistake,’’ Cardinals manager Tony La Russa said.

Albert Pujols went 0-for-4 to snap his 10-game hitting streak.

The Reds, who had three hits in a 2-1, 10-inning win at Arizona on Sunday, strung together that many in the sixth inning while wiping out a 1-0 lead. Arroyo led off with a single, but was eliminated on Chris Dickerson’s force-play grounder. Jerry Hairston Jr. singled and Joey Votto walked to load the bases. Encarnacion took the first two pitches from Looper for strikes and the third, which narrowly missed, before lining a double into the left field corner.

‘‘I felt like I was in control the whole time,’’ Looper said. ‘‘I don’t know what happened in the sixth, Even then, I felt like I was in control. They found some holes and then I made a bad pitch … and Encarnacion made me pay.’’

Troy Glaus, day-to-day with a strained right shoulder, wasn’t in the Cardinals’ original starting lineup, but he felt well enough to play after taking batting practice. He proved it by leading off the second inning with his 24th homer of the season and first since Sept. 3, giving St. Louis a 1-0 lead.

Aaron Miles cut Cincinnati’s lead to 3-2 with his fourth homer of the season in the seventh inning. The Reds got that run back in the bottom of the inning, when Corey Patterson scored from third base as pinch-hitter Danny Richar beat out a potential inning-ending double-play ball.

Patterson added a two-run double and pinch-hitter Javier Valentin drew a bases-loaded walk in the eighth inning.

Notes: The Reds honored LHP Tom Browning on the 20th anniversary of his perfect game against the Dodgers, the only perfect game in franchise history. Fans received a Browning bobblehead doll, and he threw a ceremonial first pitch. … Rookie RHP Ramon Ramirez will start for Cincinnati Friday against Milwaukee. Rookie RHP Johnny Cueto, who was scheduled to start Friday, will start Saturday. … Glaus replaced rookie LF Nick Stavinocha in the batting order. Felipe Lopez, originally scheduled to start at third, was moved to left field.