Chicago, IL (Sports Network) - Mark Buehrle was solid on the hill and Paul Konerko had a home run to keep Chicago's playoff hopes alive, as the White Sox beat Cleveland, 5-1.

Minnesota beat Kansas City on Sunday, 6-0, meaning the White Sox are one-half game behind the Twins for the AL Central lead. Chicago will host a makeup game with Detroit on Monday to help crown the AL Central champions.

Should a tiebreaker between the White Sox and Minnesota be necessary, it will be played in Chicago on Tuesday.

Buehrle (15-12) lasted seven innings and gave up a run on nine hits with six strikeouts and one walk to get the win.

Jermaine Dye had a pair of RBI for the White Sox, who saw their five-game skid become history.

Bryan Bullington (0-2), who was named as a last-minute replacement for likely AL Cy Young Award winner Cliff Lee, who was scratched with a stiff neck, took the loss after getting tagged for three runs -- two earned -- on five hits in five frames.

Jhonny Peralta's solo homer accounted for all the offense for Cleveland, which finished the season at 81-81 for third place in the AL Central. Franklin Gutierrez went 2-for-3 in defeat.

The Tribe took a 1-0 lead in the second inning as Peralta led off with a blast over the fence in right field.

The Pale Hose answered in the home half. Konerko knotted it up as he pulled a ball down the line in left that just stayed inside of the foul pole for a solo shot.

Ken Griffey, Jr. followed with a double and Alexei Ramirez drew a walk before AJ Pierzynski loaded the bases with a single. Juan Uribe reached on a fielding error by Jamey Carroll, which allowed Griffey to score, and Orlando Cabrera's sac fly made it 3-1.

Uribe had a one-out single in the seventh and moved to third as Cabrera followed with a single. DeWayne Wise grounded out to make it second and third, and Dye's single scored both runners to give the ChiSox a 5-1 cushion they did not surrender.