Rollins, in camp on a Minor League deal, continued his hot spring. He got on base three times as he had a single and a walk in addition to the home run, his second this spring.
San Diego first baseman Wil Myers recorded his first hit of spring when he lined a single to center field in the fourth inning. Myers started the spring 0-for-14. He later added an RBI double.
Dioner Navarro added a two-run double for the White Sox, who improved to 6-3-1 in Cactus League play. The Padres are now 2-8-1.
Shields, the Padres' No. 2 starting pitcher, allowed four runs on six hits over 2 2/3 innings with two walks and one strikeout.
"I didn't feel great as far as mechanical stuff. I just wasn't really that sharp," Shields said. "I was trying to throw a lot of fastballs today, for the most part. A few changeups, a couple cutters, I threw maybe one curveball today. But I just wasn't locating.
"I was trying to work on fastball command on the inside part of the plate to lefties today, and I was just missing. I've got to be better."
Cory Spangenberg hit an RBI double in the sixth inning as the Padres avoided being shut out.
Up next for White Sox:Erik Johnson gets the start for the first of six games between the Cubs and White Sox to be played this season, with the first pitch scheduled for 2:05 p.m. CT in Mesa, Ariz. Jason Benetti will make his broadcast debut for the South Siders. Mat Latos will start in a "B" game Saturday morning in Surprise, Ariz.
Up next for Padres: The Padres face the Indians for the second time in three days when they play a 1:30 p.m. PT game on Saturday at the Peoria Sports Complex. Andrew Cashner is coming off an outing on March 7 when he tossed two scoreless innings against the Brewers in his first outing of the spring. Cashner, the No. 3 starter in the rotation, has reverted back to his old spike curveball from the past and threw several for strikes the last time out.
Corey Brock is a reporter for MLB.com. Keep track of @FollowThePadres on Twitter and listen to his podcast. This story was not subject to the approval of Major League Baseball or its clubs.