The White Sox managed just five hits off the Devil Rays and starter Victor Zambrano, but scored three runs, which was enough for starter Bartolo Colon, who gave up one run over 6 2/3 innings.
A second-inning leadoff error by Marlon Anderson on a Carl Everett grounder started things off for the Sox, who two strikeouts and two walks later, went up 2-0 with a Roberto Alomar single. Everett, who went 0-4, stole his fifth base of the season in the inning.
Colon coasted through the first four innings before long fifth and sixth innings took its toll in the seventh with a Julio Lugo solo home run. All of Tampa Bay's runs came by homers from Lugo and Crawford, who had three homers combined coming into the game.
Damaso Marte replaced Colon after a 119-pitch effort, throwing 1 1/3 scoreless innings. Colon struck out seven, walked one and gave up eight hits.
The Sox added their third and final run in the top of the ninth on Brian Daubach's fifth home run of the season. Daubach had two of the Sox' five hits, with Roberto Alomar going 2-3 and Jose Valentin going 1-3.
The ninth-inning collapse started safely enough with a strikeout, but a walk and single later brought up Crawford, who ended the game with a homer to right, winning 4-3.
Game two of the series will be played on Saturday at 5:15 p.m. CT, with Esteban Loaiza going up against Jorge Sosa. The game will be televised on WGN.