Juan Francisco had a two-run single and Minor (1-0) won his first start of the season, allowing one run and five hits in 7⅓ innings. He walked none and struck out seven.
Eric O’Flaherty got two outs in the eighth and Craig Kimbrel threw eight pitches in a perfect ninth for his second save.
Making his Cubs debut, Scott Feldman (0-1) threw two wild pitches, hit a batter and had a fielding error in the fourth when he missed the bag in an attempt to cover first base.
Feldman gave up four runs, five hits and four walks in 4⅔ innings.
Upton’s shot gave the Braves a 1-0 lead in the first. His sacrifice fly in the third drove in Andrelton Simmons to make it 2-0.
Feldman could only blame himself for the second run. He issued a leadoff walk to Simmons, who stole second and advanced to third on a wild pitch.
Minor’s one costly mistake came when Scott Hairston led off the fifth with a homer, his first, to make it 2-1.
Since the beginning of September last year, Minor is 5-0 with a 0.94 ERA in six starts. He also improved to 5-0 in five career starts against the Cubs.
Francisco used an inside-out swing with one out in the fifth to drive the ball into left field for a two-run single that made it 4-1.
That hit chased Feldman, who threw balls on 49 of his 102 pitches. Michael Bowden ended the inning on rookie Evan Gattis’ groundout.
Bowden faced the minimum over the next 2⅓ innings. Hector Rondon faced four batters in the eighth.
Feldman, who spent his first eight seasons with Texas, is 0-6 with a 6.85 ERA over his last nine starts.