Winning for the third time in his last four starts, Lester, 13-8, scattered eight hits over seven innings, allowing the Tigers only run to score in the second inning.
The Red Sox came back with two runs off Scherzer, who was seeking his 20th win, in the fifth, when Will Middlebrooks singled with two outs, bringing home Jonny Gomes and Stephen Drew.
Lester fanned nine and didn't walk a batter. Both starters threw 111 pitches.
The win kept he Red Sox 5 1/2 in front of Tampa Bay in the East, with the best record in the AL at 83-57. The Tigers have a 7 1/2 game bulge in the Central over second place Cleveland.
Game three of the series is scheduled for 7:00 pm EDT, Wednesday at Fenway Park.
Bailey started out the game in rough fashion, opening up the game by giving up a single to Carpenter and walking Carlos Beltran. After fanning Matt Holliday, he induced a double play to end the inning. In the second, Bailey plunked Jon Jay with one out in the second and gave up Carpenter's second single with one down in the third, but he was perfect after that, setting down the next 14 batters in order before turning the ball game over to the Reds' relievers.
Bailey fanned eight and issued just the one walk to Beltran in the first inning, improving to 10-10 on the year. Only he and San Francisco's Tim Lincecum have thrown no-hitters this season, both coming in July. Bailey shut down the Giants, 3-0, on July 2nd, inspiring Lincecum to do the same to the Padres on July 13.
The loss dropped the Cardinals two games behind the Pirates in the NL Central, while the Reds remained 3 1/2 back. Pittsburgh guaranteed itself a winning season with their 81st win, a 4-3 victory at Milwaukee. The Pirates last winning season was 1992.
The Reds host the Cardinals in game three of the series at 7:10 pm EDT on Wednesday night.
Today's Trivia: Who led the National League in hits more times, Pete Rose or Tony Gwynn? (answer tomorrow)
Yesterday's Answer: Pete Rose became the all-time hits leader in 1985.