The White Sox are now four games out of first place at 52-50; the first time they've been two games over .500 since May 1.
Jon Garland started the game for the Sox, throwing seven innings and allowing two runs.
Garland struck out two and walked three while giving up four hits. Garland threw 99 pitches.
The first run came on back-to-back walks to start off the third, setting up a Frank Catalanotto RBI-groundout after a Howie Clark sacrifice bunt. The Blue Jays went up 2-0 in the fifth with a homer by Eric Hinske.
With that, like Wednesday, the Sox found themselves coming from behind. The deficit was 2-0 and the inning was the sixth, which is when singles by Carlos Lee and Ordonez set up a Carl Everett RBI-double and Paul Konerko RBI-groundout.
Between the Ordonez and Everett at bats was a rain delay that lasted 20 minutes - the amount of time needed to close the dome and perhaps cool off an effective Kelvim Escobar. Escobar threw seven innings, giving up two runs.
And after the tying runs came six scoreless innings from both staffs, using a combined total of nine relievers.
Damaso Marte, Tom Gordon and Rick White came in on the Sox' end, giving up one run -- a 13th-inning homer by Vernon Wells off White -- over six innings. Marte threw 2 2/3 innings and Gordon 2 1/3 innings. White picked up the save, his first since June 12, 2001.
The Sox' 13th started with a Lee ground-rule double. Thomas then hit a single up the middle to score Lee and Ordonez doubled to right-center, scoring Thomas, who was running on the pitch. Tanyon Sturtze gave up the runs and was charged with the loss.
Of the 12 hits for the Sox, four came from Ordonez, while Lee and Thomas had two each. Roberto Alomar, Everett, Konerko and Joe Crede each had a hit. Jose Valentin went 0-6 with four strikeouts. Willie Harris pinch-ran and stole his ninth base.
The Sox will now head back home to host the Devil Rays for a three-game set starting Friday at 7:05 p.m. CT. Esteban Loaiza is scheduled to pitch against Jorge Sosa. The game will be televised on Fox Sports Net.