CHICAGO -- Tired and beat up, the Texas Rangers looked the part for the first three innings.

Then a hit. Then another. And Mitch Moreland hit a tying, three-run homer. Just like that, the Rangers were on their way to a 7-4 win over the Chicago White Sox on Friday night.

Josh Hamilton hit a tiebreaking home run in the sixth, and Moreland added a two-run shot to tie a career high with five RBI for the Rangers, who rallied for their 10th win in 12 games despite another shaky performance from starter Matt Harrison.

Oh, and the Rangers didn't get to their hotel until 6:30 in the morning.

"It's not so much the physical part of it, because you know you're physically tired. We played a tough ballgame last night. It just took us a few innings to get back in a groove."

"A few runs will always do it for you."

Reliever Yoshinori Tateyama (2-0) pitched 2 2/3 scoreless innings and Neftali Feliz pitched a scoreless ninth for his 25th save in 31 chances.

Moreland sat out the Thursday finale against the Angels with a tight right hamstring, but showed no ill effects while trotting around the bases on Friday.

"They just said be smart with it," he said. "I've just been trying to work, slow stuff down and not press a whole lot in the box."

The White Sox have lost three of four and are five games behind AL Central-leading Detroit.

Jake Peavy (5-6) allowed seven runs and six hits in six innings. He is 0-4 in his last six outings at home.

After making a great catch in the outfield in the fifth inning to rob Carlos Quentin, Hamilton led off the sixth with a towering home run to right. It was Hamilton's 16th of the season. Two outs later, Mike Napoli singled off Peavy and Moreland connected on a 2-0 pitch for his second homer of the game and 16th of the season to give the Rangers a 7-4 lead. It was Moreland's third career multihomer game.

Peavy couldn't hold a 3-0 lead in the fourth inning, Michael Young hit a two-out single for the Rangers' first hit of the game. Nelson Cruz doubled off the wall in left to score Young from first. Peavy walked Napoli and Moreland followed with a three-run shot, giving the Rangers a 4-3 lead. Moreland was back in the lineup after missing Thursday's game with tightness in his right hamstring. Peavy didn't allow a home run in his previous seven starts.

The White Sox came back in the fifth inning by taking advantage of shortstop Elvis Andrus' fielding error. With a runner on first, Juan Pierre placed a bunt right in front of catcher Yorvit Torrealba who threw a strike to Andrus covering second. But the ball went off his glove into center field, allowing Gordon Beckham to go to third. Brent Lillibridge followed with a sacrifice fly to tie the game at 4. After a walk to Paul Konerko, Harrison was pulled for Tateyama, who was helped by Hamilton. With runners on first and second, Hamilton made a running catch into the center-field wall to rob Quentin. Tateyama ended the inning by getting Alexei Ramirez to pop out.

Tateyama inherited two runners in the fifth after Harrison was removed. Carlos Quentin greeted him with a deep drive to center field, but Josh Hamilton retreated and made a running grab as he crashed into the wall.

"That was quite a play right there, we certainly needed it," Washington said of Hamilton's run-saving grab. "Quentin just didn't get enough of it. What it ended up being is what we needed right there -- an out."

Harrison lasted just 4 1/3 innings, allowing four runs -- three earned -- and four hits with three walks.

"I don't feel like I did my job tonight," Harrison said. "It's definitely frustrating coming off my last outing, only going 5 1/3, and tonight not being able to get out of the fifth."

The White Sox tagged Harrison for two runs and three hits in the first inning. Pierre led off with a bunt for a single and stole second. After a walk to Konerko, Quentin doubled down the left-field line to score Pierre. Ramirez followed with a single to give the White Sox an early 2-0 lead.

The trouble continued for Harrison in the second. Brent Morel tripled off the wall in center and scored on Pierre's safety squeeze bunt.

But then the sleepy Rangers woke up.

"That just shows the mentality of this team," Moreland said. "We go out and we're going to fight it. There's no game that we think is out of reach."

Notes

• Harrison gave up six runs in 5 1/3 innings in Sunday's 7-6 victory over Oakland.
• White Sox LHP John Danks, who is scheduled to start Saturday, is 5-1 with a 2.29 ERA (14 ER/55.0 IP) over his last nine starts, compared to 0-8 with a 5.25 ERA (41 ER/70.1 IP) in his first 11 starts.
• RHP Alexi Ogando will try to become the first Rangers starter to win 13 games this season and just the ninth Texas right-hander to reach that mark over the last 10 seasons in his start Saturday against the White Sox.
• Before Friday, the last time Peavy gave up a home run was June 30 in Colorado.
• Ramirez was ejected by home plate umpire Jeff Nelson after he argued a called third strike in the eighth.