CLEVELAND -- Indians manager Terry Francona likes to talk about grind-it-out wins.
Tuesday night's 5-3 victory over the Boston Red Sox fit that category perfectly.
Michael Bourn's two-run double in the seventh inning snapped a 3-all tie and extended Cleveland's winning streak to a season-high five straight games.
The Indians scored three runs on five straight hits in the first off Jake Peavy, but couldn't add to the lead and the Red Sox tied the game in the seventh. The deadlock didn't last long.
''We played a good game,'' Francona said. ''I thought we had to. We strung together a number of hits (in the first), then you're kind of hanging on for dear life. When they tied it, we came back.''
Cleveland (29-30) can get back to .500 for the first time since April 24 if it can complete a three-game sweep Wednesday. The Indians have made up six games in the AL Central standings since May 18 and trail first-place Detroit by 4½ games.
Francona always stresses to his players to take things one day at a time.
''That's the only way you can dig yourself out of a hole,'' he said. ''It can look so daunting when you look too far in advance, but when you take care of what you're supposed to do that day, all of a sudden things can mount in a good way.''
The Red Sox have lost two straight after winning seven consecutive games. That streak was preceded by a 10-game losing streak.
Nick Hagadone (1-0) struck out three in 1 1/3 innings. Cody Allen recorded the final four outs for his fifth save, striking out former Indians All-Star Grady Sizemore, pinch-hitting for Jonny Gomes, to end the game.
Allen also retired Sizemore for the final out in Monday's 3-2 win.
''Obviously, they have some very good hitters,'' Allen said. ''They're the defending world champions. That's a veteran group. They have a lot of wins over there.''
Peavy (1-3) allowed five runs in 6 1/3 innings. The right-hander, who hasn't won since April 25, gave up three runs in the first, but held the Indians scoreless until the seventh.
David Murphy walked to start the inning and Yan Gomes singled. Peavy threw out Murphy at third on Mike Aviles' sacrifice attempt, leaving runners at first and second. Andrew Miller relieved, but Bourn doubled off the lefty over the head of Gomes in left field to score both runners.
''Bournie had a really good at-bat,'' Francona said. ''That's not a fun lefty to face from the left side.''
Bourn, who hit a walk-off homer Sunday against Colorado, is 8 for 19 with five RBI in Cleveland's winning streak. The Indians are 20-11 at Progressive Field, the best home record in the AL.
Peavy, who was 0-2 with a 5.89 ERA in six starts last month, retired 14 in a row at one point, a stretch that ended with Chisenhall's two-out single in the seventh.
''This is a tough one to lose,'' Peavy said. ''I don't know if I've ever started a game with five straight hits. Tonight was a grind.''
Xander Bogaerts hit a solo homer with one out in the third. Jonathan Herrera's sixth-inning single cut the lead to 3-2. Bogaerts started the seventh with a double off Scott Atchison and scored when Dustin Pedroia doubled.
Cleveland starter T.J. House allowed two runs in 5 2/3 innings.
Boston pitcher Brandon Workman appealed a six-game suspension imposed by Major League Baseball on Tuesday for throwing near the head of Tampa Bay star Evan Longoria last week. Workman can play until the appeal process is complete, and is expected to make his scheduled start Wednesday night in the series finale. ... Indians 3B/C Carlos Santana (concussion) took batting practice and ran the bases Tuesday. He could be activated Friday. .... Boston C Ryan Lavarnway (fractured left wrist) underwent surgery Tuesday in Cleveland to remove his hamate bone. Manager John Farrell expects a five-to-seven week recovery period before baseball activities take place. ... 1B Nick Swisher (sore left knee) could go on a minor-league rehab assignment next week. He has begun to play catch and is scheduled to start hitting in a couple of days. ... Browns rookie quarterback Johnny Manziel will throw out the first pitch Wednesday.