The team said that X-rays revealed Revere had a broken right foot, and that Revere will see a specialist Monday.
"Ben is very important, and this is a big blow to us," manager Charlie Manuel said after the second game.
After a slow start, Revere had turned the corner. Since May 1 he was batting .347 (78 for 250), raising his average from .200 to .305. He had hit safely in 14 of his last 15 games, and was batting .431 during that span with 10 multihit games. He has also stolen a team-high 22 bases.
John Mayberry Jr. started in center in the second game, but it will be interesting to see what the Phils do.
Earlier this month, second baseman Cesar Hernandez started to play a few games in center field for triple-A Lehigh Valley. Hernandez was with the Phillies earlier this year when Chase Utley was out.
As for the game, the Phillies failed to take advantage of chances in the ninth and 10th innings before finally falling in the 11th.
The second game also went to extra innings and ended too late for this edition.
"We had some golden chances and all we had to do was hit the ball and we couldn't do it," Manuel said. "The game was sitting there for us two or three times."
Chicago's Alejandro De Aza hit a two-out triple off J.C. Ramirez in the 11th and scored on Alexi Ramirez's double. Ramirez then scored the White Sox' fifth run when Jimmy Rollins booted a grounder by Alex Rios. That run would prove to be the difference.
Darin Ruf, who was 3 for 4 with a home run and two runs scored, opened the Phillies 11th with a double off Addison Reed and scored on a one-out pinch-hit single by Humberto Quintero. Revere then hit into the game-ending double play.
The Phillies were 2 for 13 with runners in scoring position. They are now 4-4 in extra-inning games and 3-10 in games this season in which they had an opportunity to reach .500.
In the 10th inning the Phillies had runners at the corners with one out, but Delmon Young struck out and Kevin Frandsen grounded out.
Phillies closer Jonathan Papelbon pitched a scoreless ninth that was followed by a 41-minute rain delay.
The Phillies then failed to score with runners on second and third and no outs in the ninth.
Frandsen and Ruf opened the ninth with singles off reliever Nate Jones, putting runners on first and second. Jones balked while lobbing a pickoff throw to second, moving the runners to second and third. Carlos Ruiz popped out to short left field for the first out. Pinch-hitter Laynce Nix struck out and Revere lined out.
The Phillies jumped on lefthander John Danks for two first-inning runs on an RBI groundout by Domonic Brown and Delmon Young's RBI single.
Chicago took a 3-2 lead on Conor Gillespie's sacrifice fly in the sixth.
Ruf tied it in the seventh with a one-out home run to center.
Contact Marc Narducci at firstname.lastname@example.org. Follow @sjnard on Twitter.