Uggla passed Rico Carty’s 31-game streak in 1970 for the longest in Atlanta Braves history when he led off the second with his 25th homer.
Zambrano (9-7) gave up eight runs and eight hits, including a career-worst five homers, in 4 1-3 innings.
Zambrano was ejected by umpire Tim Timmons in the fifth inning after throwing two inside pitches to Chipper Jones, the second going all the way to the backstop.
The brush-back pitches followed homers by Freddie Freeman and Uggla.
Jones and Jose Constanza also went deep against Zambrano.
Starlin Castro homered and Alfonso Soriano had two RBIs for the Cubs, who had won nine of 11.
Uggla went 3 for 3 and scored three times. His streak, which began on July 5, is the longest in the majors this season. He has raised his batting average from .173 to .229.
Tommy Holmes holds the franchise record with a 37-game hitting streak as a member of the Boston Braves in 1945.
Atlanta grabbed control with three runs in the third. Zambrano retired the first two batters before Freeman singled and Uggla was hit by a pitch. Jones then hit a drive to center for his 10th homer, making it 5-1.
Freeman and Uggla hit back-to-back homers in the fifth to give Atlanta an 8-1 lead.
Zambrano then threw one pitch inside to Jones and was immediately tossed after the Atlanta star had to jump back to avoid another inside pitch.
As Jones stood at the plate, staring at Zambrano, the Braves came out of their dugout. Timmons rushed toward the dugout, cautioning the players not to come out any farther.
Zambrano looked back at Jones as he walked off the field, then was shown on TV smiling before leaving the dugout for the clubhouse.
Zambrano dropped to 2-5 with a 6.08 ERA in 13 career starts against Atlanta. The right-hander has dropped his last five decisions against the Braves.
Atlanta rookie Mike Minor (2-2) gave up three runs and nine hits in 5 2-3 innings.
The left-hander allowed three hits in the sixth, including a two-run double by Soriano. Braves left fielder Martin Prado almost caught Soriano’s drive, but the ball bounced out of his glove when he crashed into the wall.
NOTES: Uggla entered Friday night’s game batting .355 (44 for 124) with 12 homers and 29 RBIs during the streak, but only .224 overall. ... Braves C Brian McCann (strained left oblique) began a rehab assignment with Triple-A Gwinnett. He was to have one game as a designated hitter, one game as a catcher and then possibly come off the DL. disabled list on Sunday. ... Jones’ homer was his 1,000th extra-base hit. ... Attendance was 50,146.