Price (20-5) became the first 20-game-winner in Rays franchise history. He limited the Chisox to two runs on five hits while striking out four.
The Cy Young Award candidate joined Jered Weaver of the Los Angeles Angels as the only 20-game winners in the American League this season.
B.J. Upton bashed two home runs and finished with three RBI as the surging Rays won their 10th in 11 games. They came into the contest three games behind Oakland for the final wild card spot in the American League.
Tampa Bay will conclude its regular season with three games against AL East co-leader Baltimore.
The Rays reached Jose Quintana (6-6) for four runs on six hits in four innings.
The fading White Sox fell three games behind AL Central-leading Detroit with three games to play.
Celebrity Couples of 2014 [PHOTOS]