CHICAGO – David Price became Tampa Bay's first 20-game winner, B.J. Upton homered twice and the Rays stayed afloat in the AL wild- card race by beating the fading White Sox, 6-2.

Tampa Bay, which began Sunday three games behind Oakland for the second wild card, won for the 10th time in 11 games. The Rays, who close at home against Baltimore, were eliminated from the AL East earlier Sunday.

The Sox have lost 10 of 12 and moved to the brink of elimination, falling three games behind AL Central-leading Detroit with three games to play. The Sox held at least a share of the lead from July 24 until Wednesday and had not been this far back since late May.

The Sox's only hope is to sweep three games at Cleveland and have the Tigers lose three at Kansas City, which would force a one-game tiebreaker.

Price (20-5) improved to 12-1 with a 2.26 ERA in his last 18 starts, allowing two runs and five hits in seven innings. He became the fourth 20-game winner of the season, joining Washington's Gio Gonzalez (21-8), the New York Mets' R.A. Dickey (20-6) and the Los Angeles Angels' Jered Weaver (20-4).

Upton hit his 27th and 28th homers, and Tampa Bay also got a solo shot from Ryan Roberts.

Sox starter Jose Quintana (6-6) got in trouble before the game was barely three minutes old, giving up a leadoff triple to Desmond Jennings and Upton's two-run homer.

Roberts hit a two-out homer in the fourth made it 3-0. The White Sox rallied in the bottom half when Alex Rios delivered an RBI single and Dayan Viciedo hit a bases-loaded sacrifice fly.

Upton's leadoff double in the fifth finished Quintana, who allowed four runs and six hits in four innings. Evan Longoria hit an RBI double and Ben Francisco added a sacrifice fly off reliever Nate Jones to make it 5-2. Upton homered again in the ninth against Addison Reed.

NOTES: Sox C A.J. Pierzynski had his family at the game. He is eligible for free agency and this might have been his final home game in Chicago. Pierzynski, who came to Chicago in 2005, said he'd love to finish his career with the  Sox but understands that might not happen. He's had a career-best 27 homers. ... Rays C Jose Molina (right quadriceps strain) was out of starting lineup for fifth straight game but caught the bottom of the ninth.