Braves' starter Tom Glavine, who got his 300th win last Aug. 5 at Wrigley while pitching for the Mets, had to leave after three innings with a left elbow strain.
Greg Norton's three-run homer in the first off Lilly gave Glavine an early cushion but with his control off and his elbow apparently hurting, he let it slip away.
The NL Central-leading Cubs rallied and are now 27-8 in their home ballpark this season. Lee had a solo shot in the third to tie the game and Soto a three-run drive in the eighth to put it away.
Glavine (2-3) gave up four runs, six hits and four walks while throwing 72 pitches in his second shortest outing of the season.
Glavine's injury came on the same day longtime teammate John Smoltz underwent shoulder surgery in Birmingham, Ala., with the team saying the future of his career is still unclear.
With Chipper Jones, batting .420, missing his second straight start with a small tear in his right quadriceps, the Braves put Omar Infante into the lineup at third. He had a leadoff triple in the second but was stranded and later added an RBI single.
Jones did pinch-hit in the seventh and drew a two-out walk to finish Lilly. Jones was replaced by pinch-runner Josh Anderson before Cubs reliever Carlos Marmol got Yunel Escobar to line out with two runners on.
Lilly (6-5) worked 6 2-3 innings to get his first win since May 19. He allowed four hits and the three runs with three walks and eight strikeouts. After Infante's triple, he retired 11 straight.
The Cubs made it 3-2 in the second on a walk, consecutive singles by Soto, Kosuke Fukudome and Mark DeRosa and Reed Johnson's bases-loaded sacrifice fly.
Lee led off the bottom of the third with his 14th homer to tie the game. After Aramis Ramirez walked and moved to third on two infield outs, DeRosa drew another walk before Johnson delivered an RBI single to right for a 4-3 lead.
Johnson wasn't through. He raced to the alley in left-center to make a great catch of Infante's liner to end the fourth. Ramirez hit an RBI single off reliever Buddy Carlyle for a 5-3 lead in the bottom of the inning. DeRosa added a run-scoring single in the seventh off Manny Acosta and the Cubs were up three.
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But the Braves came back off Chicago reliever Bobby Howry with four singles in the eight, including two-out RBI hits by Brian McCann and Infante that made it 6-5 before Scott Eyre fanned Gregor Blanco.
Alfonso Soriano singled, stole second and went to third on McCann's throwing error. After Ryan Theriot reached on Acosta's error to put runners at the corners, Lee hit a sacrifice fly. After Ramirez was walked intentionally before Soto hit his 11th homer.
Norton made just his 11th start of the season and was batting .176 when he connected on his second homer of the season, a two-out shot that gave Glavine some working room.
After Norton homered, Lilly's next pitch went over the head of McCann and home plate umpire Doug Eddings jumped out and immediately warned both benches. As Glavine was warming up to start the bottom of the first, Braves manager Bobby Cox came out and chatted with Eddings.
Notes: Glavine's shortest outing this season came on April 13 when he did not record an out against the Nationals. ...The Cubs are 41-24. Through 65 games a year ago, they were 30-35. ... The Braves are a major league-worst 7-22 on the road. They have lost four straight overall.
[Associated Press; By RICK GANO]
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