The White Sox earned a 3-2 decision in the opener of this twinbill, which made up games postponed on April 27 and 28 due to last month's Baltimore riots, behind Chris Sale's 7 2/3 scoreless inning, 12-strikeout effort.
Ryan Flaherty also had two hits while scoring a run for Baltimore in the nightcap.
All three Chicago runs in Game 2 came on a pair of homers off Mike Wright (2-0) in the rookie's five-inning stint. Four Oriole relievers combined to hold the White Sox scoreless the rest of the way, with Zach Britton twirling a perfect ninth to nail down his 13th save.
Chris Beck (0-1) was able to give the White Sox six innings in his major league debut, but was reached for five runs -- four earned -- and 10 hits while walking four.
LaRoche's blast, a towering drive off a hanging curveball from Wright with Melky Cabrera aboard in the third inning, staked Chicago to a brief 3-2 lead that Beck wasn't able to hold in the bottom of the frame.
An Adam Jones single and a walk to Chris Davis put two men on for Clevenger, who shot a base hit through the left side in which Jones scored as White Sox catcher Geovany Soto mishandled Cabrera's throw home. J.J. Hardy followed with a single off third baseman Conor Gillaspie's glove that brought in Davis for a 4-3 Baltimore edge.
Wright retired seven of his final eight hitters after serving up LaRoche's homer, but reliever Oliver Drake walked the first two White Sox in the sixth with the margin still at one. Gordon Beckham was doubled off first on Gillaspie's flyout to right, however, to help kill a potential scoring opportunity.
Baltimore expanded its advantage when Flaherty doubled in the bottom of the sixth and came around on Snider's two-out single. Another run was produced after hits by Clevenger and Flaherty in the seventh preceded Lough's infield single that increased the lead to 6-3.
Wright had tossed 14 1/3 scoreless innings over his first two outings, though that streak came to a swift end when Eaton drove his fifth pitch of the day over the wall in left. Manny Machado tripled to right on Beck's initial offering in the big leagues, however, and crossed the plate on Jones' slow grounder to forge a 1-1 tie.
Davis, whose two-run homer in the ninth accounted for the Orioles' only offense in Game 1, then socked a ground-rule double that knocked in Jones.