Jon Lester struck out 10 over seven innings as the Cubs improved to 17-5, their top 22-game start since the 1907 team was 18-4.
In a matchup of the clubs with the best and worst records in the majors, the Braves fell to 5-18.
It was 1-all in the eighth when the Cubs loaded the bases on two hits and a walk against Jim Johnson (0-3). Lefty Eric O'Flaherty relieved and gave up Anthony Rizzo's go-ahead single with one out.
Szczur then followed by launching a pitch from Chris Withrow over the left field wall.
Freddie Freeman's solo shot in the fourth was only the Braves' fifth home run of the season.
Pedro Strop (1-0) pitched a perfect eighth.
