Harrison has two of those six victories and has now pitched 10 consecutive scoreless innings over his past two starts.
"He made pitches when he had to make pitches," Rangers manager Ron Washington said. "Give them credit. They made him work. He only gave us five innings, but they were five pretty good innings."
Harrison allowed six hits and hit a batter. He was dealing with baserunners in every inning, and the White Sox had runners in scoring position in three of the five innings. But Chicago was 1-for-8 against him with runners in scoring position.
The big inning was the fifth. The Rangers led, 4-1, but the White Sox loaded the bases on three consecutive singles. Harrison came back to strike out Josh Fields, and then, on a full-count pitch, retired Carlos Quentin on a flyout to right to end the threat.
"What did I see out of him?" Guillen said of Harrison. "He throws strikes. He was in deep counts all the time and walking people. But he got the win. To me, whoever got the 'W', that's the one who is the best. I don't care how good or bad he throws."
Harrison threw 100 pitches over five innings, which is why the Rangers went with Jason Jennings to start the sixth.
"That's a lot more pitches than I wanted to throw in five innings," Harrison said. "I'm pleased with five scoreless, I just wish it could have been longer. Hopefully I can keep going with what I'm doing."
Mainly Harrison won because he was able to throw his sinker over the low outside corner of the plate to right-handed hitters, something that was missing in his first few starts. He was also able to pitch inside effectively, something the Rangers tried to do the entire series. They ended up hitting four batters in the past two games, including three on Saturday night.
Harrison hit Fields on the hand in the first inning. The White Sox did not hit a Rangers batter.
"That shows people I'm not a headhunter," Guillen said. "I don't think they try to hit anybody. They honestly don't, because if they will, I will let them know right away. They try to pitch in, and unfortunately, they hit us, but you can't control that. You get upset and you get mad because your players are getting hurt. But in the meanwhile, that's part of the game. They don't try to hit anyone. They try to pitch in and we can't do nothing about it."
Harrison beat John Danks, the former Rangers first-round pick in the 2003 First-Year Player Draft who gave up a leadoff home run to Ian Kinsler in the first inning and five runs in 5 1/3 innings on the night. The 10 hits were the most he's ever given up in a game in 64 Major League starts, and he is now 1-2 with a 5.30 ERA in three career starts against the Rangers.
"It's always been just another start," said Danks, traded to the White Sox after the 2006 season. "I have more at stake than worrying about what these guys are doing or thinking or trying to impress someone. I have my own career to worry about. I really don't care what these guys think. I'm just going out there to try to give us a chance to win."
Kinsler hit a 3-2 fastball over the left-field wall in the first for his ninth home run of the year. It's also the eighth time in his career he has hit a home run to lead off the first inning, tying a club record set by Mike Hargrove, Oddibe McDowell and Michael Young.
"I'm not trying to hit a home run in my first at-bat," Kinsler said. "I'm trying to drive the ball every single at-bat. I like doing that, though. Hitting one out of the ballpark in the first at-bat takes some air out of the other team and helps your starting pitcher relax, knowing he already has a 1-0 lead."
The Rangers added four more runs. Nelson Cruz had a three-hit night, Young snapped an 0-for-15 with runners in scoring position with an RBI single, and Elvis Andrus had two hits and a sacrifice bunt in his first game as the No. 2 hitter in the order. Manager Ron Washington thought moving Andrus to the No. 2 hole -- at least against left-handers -- while Josh Hamilton is out might allow the Rangers to take advantage of the rookie shortstop's ability to do multiple things offensively.
That's what happened. Andrus scored in the third inning after a one-out double and a steal of third base, and his sacrifice bunt after Kinsler's infield single set up Young's hit.
"I like it," Andrus said. "All my career I have been hitting second. I feel comfortable there and we got the win."