Galarraga pitched 6 1/3 scoreless innings, leading the Detroit Tigers past the White Sox 9-0 to end Chicago's three-game winning streak.
"He was very good, but we let him off the hook too many times," White Sox manager Ozzie Guillen said. "He's a good pitcher, but we were chasing his slider when we needed hits."
Miguel Cabrera went 3-for-5 with a homer and two RBIs for the Tigers.
Galarraga (2-0) gave up four hits and two walks while striking out five. He left to a standing ovation after walking Paul Konerko with one out in the seventh.
"He was tremendous," Tigers manager Jim Leyland said. "He had late life on his pitches. It was darting and moving late in the strike zone, just at the right time. They've hit a lot of our mistakes out of the ballpark, and we were able to eliminate that today."
Jose Contreras (0-2) allowed five runs -- three earned -- and five hits in 5 2/3 innings.
"I thought Jose threw the ball absolutely well," Guillen said. "But with the Tigers, they are such a good-hitting team that you've got to stay right on top of them for all nine innings and we didn't do that."
Detroit took a 2-0 lead in the fifth inning. Josh Anderson and Ramon Santiago walked, and after Curtis Granderson hit into a force at second, Placido Polanco sent a shot over Brian Anderson's head in center for a two-run double.
"I think that shows the importance of speed," Leyland said. "That's something we were missing before, but with Josh Anderson at the bottom of the lineup -- I thought it created some problems for them. It makes the pitcher worry more about holding him on."
The Tigers made it 5-0 in the sixth on Cabrera's leadoff homer and a two-run single by Santiago. Cabrera provided the sixth run with an RBI single in the seventh, and the Tigers made it 9-0 with three runs in the eighth.
"When you get a lead, it is huge when you can keep chipping away and adding to it," Gerald Laird said. "We put up two runs, and then we put up three more in the next inning. That is kind of like a knockout blow."
Both teams had early scoring chances. Josh Fields tripled with one out in the first, but Galarraga struck out Carlos Quentin and Jim Thome. Detroit had runners on second and third with no outs in the third, but Santiago struck out, Granderson popped out and Polanco grounded out.
Galarraga escaped trouble again in the fifth, getting out of the inning after the White Sox put runners on second and third with one out.
"He made every pitch he needed to make," Fields said. "We got some runners on base, but then he shut us down. That's what we saw on film from him -- he's really good."
The Tigers paid tribute to Mark Fidrych, who died Monday, with a moment of silence and a special video before the game. ... Tigers rookie Ryan Perry was wild after entering the game in the eighth inning, causing Alexei Ramirez, Brent Lillibridge and Fields to duck pitches near their heads. Fields took a step toward the mound after avoiding the first of Perry's two wild pitches, but order was quickly restored. "We knew he was a young kid trying to throw very hard," Fields said. "I didn't think he was trying to hit anyone, but after about the fourth pitch near one of our heads, I just wanted to tell him to calm down a little." ... In the bottom of the inning, Mike MacDougal hit the backstop with a fastball.