Lee played left field. Jeff Liefer, originally scheduled to start in left, went to Ordonez's usual spot in right.
"I actually worked a little harder in batting practice and before the game because it was my day off," Lee said. "It seems like that work paid off."
The Sox scored all their runs on late-inning homers. After Lee's blast, Joe Crede hit another two-run homer in the sixth for a 4-2 lead. Frank Thomas, restored to the lineup after two games on the bench, made it 5-2 in the seventh when he hammered his 21st of the season.
Tampa Bay's Jared Sandberg, nephew of former Cubs star Ryne Sandberg, hit a solo homer for the game's first run.
Dan Wright (9-11) was the winner. He struck out eight, tying a season high, walked three and allowed five hits and two runs and 71/3 innings.
"[Catcher] Josh Paul did a nice job mixing calls, and I got pretty good location on my fastball," Wright said.
Manager Jerry Manuel said he was pleased with Thomas, who went 1-for-4 and is hitting .231 for the season.
"Frank had an excellent batting practice," Manuel said. "Now it's a matter of his getting confidence and getting pitches."
Thomas lifted some fans off their seats in the first inning. He drove Paul Wilson's pitch almost 400 feet to dead center, but Randy Winn caught the ball on the warning track.
Sandberg led off the Rays' second with his 16th home run of the season.
The White Sox stranded three runners in the bottom of the inning. Lee singled and Liefer and Paul walked, but Willie Harris popped up on Wilson's first pitch.
Wright loaded the bases with nobody out in the fourth, but the Rays scored only one run and might not have scored if Aaron Rowand had made a more accurate throw home on Toby Hall's sacrifice to short center.
Wright and Manuel both said holding Tampa Bay to one run in the fourth was critical in the game.
"Giving up a lot of runs in one inning has been a problem for me all season," Wright said. "I was hoping for ground balls, but it was nice to get out of it the way I did."
In the sixth, fans were still booing Thomas for striking out when Lee jolted Wilson's pitch over the center-field wall. He scored behind Jose Valentin, who had walked, tying the game 2-2.
The tie didn't last long. Liefer singled to left and Crede hit the second two-run homer of the inning to give the Sox their first lead.
Next, the Big Hurt came through. Down 1-2 in the count in the seventh, he lined Wilson's pitch over the wall in left.
Coming home: General manager Ken Williams said that if the players strike on Friday when the team is in Detroit, the Sox will fly them back to Chicago.
"We aren't obligated to do that," Williams said, "but we're a team, and we feel it's our responsibility to bring them back as a team."
It had been reported that players would have to arrange their own transportation if they were on the road when the strike began.
Youth is served: Williams tabbed Miguel Olivo, a 24-year-old catcher from the Dominican Republic, as one of the bright lights in the Sox's farm system. Playing for Double-A Birmingham, Olivo has starred behind the plate and at bat, hitting nine triples and stealing 27 bases.
Asked to evaluate the recent play of Harris at second and Crede at third, Williams said: "I'm glad to see they're relaxing and starting to have a little fun. At first they put too much pressure on themselves."