Steve Kemp drove in five runs with a bases-full home run and a sacrifice fly to carry Chicago over California in Anaheim.
Reliever Kevin Hickey saved the game by retiring Reggie Jackson on a grounder with two runners in scoring position for the final out. Earlier in the ninth inning, Rod Carew's RBI single off Salome Barojas had cut the California deficit to one run.
Carew extended his hitting streak to 23 games with run-scoring singles in the seventh and ninth innings. The streak is the longest in Angels history and ties Minnesota rookie Kent Hrbek for the longest in the majors this season.
A two-run homer by Jackson, his 12th of the season, had California in front, 4-2, when the White Sox loaded the bases in the fifth inning against loser Geoff Zahn on Harold Baines' infield single, a hit batsman and a walk. Luis Sanchez relieved Zahn and struck out Ron LeFlore, but Tony Bernazard singled to pull Chicago within one run. Kemp followed by propelling a 3-1 pitch over the center field wall for his sixth homer of the year and fourth grand slam of his career.
Gaining the decision over Zahn (7-3), who yielded five runs on five hits in four innings, was Richard Dotson (3-7). The Chicago right-hander worked the first 6 2/3 innings, allowing four earned runs on eight hits, to end a personal four-game losing streak. Hickey got his third save.