Published: Sep 30, 2012 5:29 PM EDT
Updated: Oct 01, 2012 6:31 AM EDT

CHICAGO (AP) - 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 Chicago White Sox 6-2 Sunday.

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

Chicago has 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 White Sox held at least a share of the lead from July 24 until Wednesday and had not been third far back since late May.

Chicago'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.