​Miguel Vargas lets it loose as he celebrates his 33rd homer of the season, giving the White Sox some much-needed breathing room. | (Geoff Stellfox/Getty Images) Sean Burke gave the White Sox a chance to win Saturday afternoon. His offense didn’t give him much support, but it gave him just enough.The righthander came out firing, mowing through the first with a fly out and back-to-back punchouts. The knuckle curve had bite, and he breezed through the first three innings on just 28 pitches.The Sox gave him a quick 1-0 lead in the bottom of the first. Miguel Vargas drew a two-out walk and promptly swiped second with Munetaka Murakami at the plate. With the stolen base, Vargas became the first player in franchise history to record at least 30 doubles, 30 home runs, 20 stolen bases, and 100 runs scored. Congratulations to Miggy! The stolen bag also proved pivotal when Mune dunked a blooper into left field, allowing Vargas to race home. Small ball, but it counts. It wasn’t exactly a fireworks show, but lately, you take the runs wherever you can find them.Jackson Jobe was every bit as stingy on the other side. The righty pounded the strike zone, fanned the side in the fourth and made the Sox look lost — except for Colson Montgomery, who at least forced a nine-pitch battle before whiffing — four innings in, still just one lonely hit for Chicago.Burke encountered his first real bit of trouble in the fourth when Hao-Yu Lee and Riley Greene singled to put runners on first and second with two outs. He escaped with help from Vargas, who made a fantastic play at third on Dillon Dingler’s grounder to end it. Vargas has endured his share of defensive struggles at the hot corner this season, recording -2 Defensive Runs Saved, but that was a gem.A 28-pitch fifth ended Burke’s efficiency. After plunking Ben Malgeri and allowing a single to Brett Callahan, he walked John Peck to pack the sacks. The breaking pitches that danced early began missing, and Kevin McGonigle lifted a sacrifice fly to left to knot things up. Burke limited the damage by striking out Lee and stranding a pair to end the frame. The White Sox immediately gave him the lead back. Braden Montgomery ripped a one-out ground-rule double and advanced to third on Brenton Doyle’s single. Sam Antonacci followed with a deep sac fly to left, putting Chicago back in front, 2-1.Would more runs be nice? Sure. But at this point, you take what you can get and say thank you.Burke returned for the sixth because, frankly, manager Will Venable didn’t have much choice. The bullpen is taxed, and asking it to nurse a one-run lead for four innings didn’t sound particularly appealing.That move nearly blew up in his face.A single and back-to-back two-out walks suddenly loaded the bases for Callahan. Burke spun a 79 mph knuckle curve that Callahan swung at, but the ball squirted away from Teel and Greene slid home with what appeared to be the tying run.Chicago challenged the call, arguing that the pitch cli