A.J. Pierzynski went 2-for-4 with an RBI for the White Sox, who were coming off a three-game sweep at Cleveland. John Danks (13-9) limited the Red Sox to one run and six hits over seven innings. The left-hander finished with five strikeouts and three walks.
Chicago moved to within 3 1/2 games of first-place Minnesota in the American League Central standings.
Marco Scutaro knocked in the lone run for Boston, which has dropped five of its last eight games.
Clay Buchholz (15-6) gave up two runs on six hits in five innings to suffer his first loss since July 21 at Oakland. The right-hander had gone 5-0 over his previous seven outings.
The White Sox got on the board in the second. Consecutive singles by Konerko and Manny Ramirez placed runners on the corners to open the inning. Konerko then came home when Pierzynski grounded into a double play.
Konerko doubled leading off the fourth, moved to third on a groundout and scored on a single by Pierzynski.
Boston cut its deficit to 2-1 in the fifth, but squandered an opportunity to pull even or seize the lead.
Bill Hall led off with a single, Darnell McDonald walked and Scutaro slapped a base hit up the middle to produce a run. Danks, though, retired J.D. Drew, Victor Martinez and Adrian Beltre in order to preserve the one-run lead.
Sergio Santos succeeded Danks and tossed a flawless eighth. Bobby Jenks gave up a leadoff single to Boston's Jed Lowrie in the ninth, but set down the next three batters to earn his 26th save of the season.
Konerko owns a 14-game hitting streak...Pierzynski has hit safely in 11 straight games...Danks matched his career high for wins in a season set in 2009...Manny Ramirez went 2-for-4 in his return to Boston.