Zaun, who finished with three of Baltimore's 11 hits, capped a four-run ninth with his fourth homer of the season.
Luke Scott had two RBI, Nolan Reimold and Cesar Izturis had one RBI apiece, two runs scored on wild pitches and Aubrey Huff had two hits for the Orioles, who averted a three-game sweep.
Winner Jeremy Guthrie (7-8) gave up two runs and just three hits in eight innings with a walk and five strikeouts.
Chicago's runs scored on solo homers by Dewayne Wise in the third and Chris Getz in the eighth. Jim Thome and Brian Anderson had the other hits for the White Sox, who had won three of four before the series began Friday.
Losing pitcher Jose Contreras (4-8) surrendered five runs and five hits in 4 1/3 innings.
Copyright 2009 by United Press International.