Eventually, the visitors broke through in the fifth, with Conor Gillaspie and Paul Konerko drawing consecutive walks to start a two-run rally. Dayan Viciedo followed the free passes with a fielder's choice grounder to shortstop Hiro Nakajima. Hector Gimenez couldn't get the run home from third on a popup to third, but Tyler Flowers' two-strike single to right broke the 0-0 deadlock.
Gordon Beckham followed with another single to right, scoring Viciedo.
Quintana was brilliant, allowing one Coco Crisp single in the third and nothing more until Yoenis Cespedes' two-out double scored Scott Sizemore in the sixth. Quintana walked three and fanned nine over 5 2/3 innings before being replaced by Ramon Troncoso.
"I felt really good and I felt like the fastball was working really good today. I worked with all my pitches but my fastball was particularly good," said Quintana through translator and White Sox coach Lino Diaz. "It was running good, especially the two-seamer to the arm side.
"Establishing the fastball is the goal for any pitcher but I pitch according to the situation as well. I tried to do a lot of physical work to strengthen my legs and I feel strong. I feel good right now and that's going to help me throughout the season."
Troncoso allowed Quintana's inherited runner to score, with a walk to Chris Young and Derek Norris' game-tying single to left. Brandon Moss followed with the go-ahead single to right, and the fourth run scored on a Troncoso wild pitch.
Parker was just as good, allowing two runs on three hits over six while striking out five.
"The outing was good," Parker said. "Being that it was night game it was a little more like it was a regular season situation. It was a little more routine in terms of what time you're getting here. I was able prep and it's a different atmosphere. I was down to two [spring] starts.I wanted to treat it like the regular season and pitch that way."
Up next: Tommy Milone will face the Giants in Scottsdale at 1:05 p.m. PT on Saturday.
Scott Merkin is a reporter for MLB.com. Read his blog, Merk's Works, and follow him on Twitter @scottmerkin. This story was not subject to the approval of Major League Baseball or its clubs.