Pedrioa then lined a pitch just beyond the reach of shortstop Alexi Ramirez, scoring both runners for Boston, which took the rubber match of a three-game series in Chicago.
The rally made a winner of Alfredo Aceves (7-1), who tossed one scoreless inning in relief of starter Andrew Miller, who had yielded three runs on 10 hits over 5 2/3 frames.
Jason Veritek belted a two-run homer for the Bosox, who lead the American League East.
Chicago starter Mark Buehrle went six innings, yielding two runs on five hits.
Ramirez, Alex Rios and Brent Morel collected RBI for the White Sox, who fell four games off the pace in the American League Central.