Minor (1-0) gave up five hits and struck out seven. Craig Kimbrel came on to work a perfect ninth and collect his second save.
Upton opened the scoring with a solo homer in the first and added a sacrifice fly in the third. A two-run single from Juan Francisco completed the Atlanta offense in the fifth.
Scott Feldman (0-1), making his first start for the Cubs, gave up four runs on five hits with four walks over 4 2/3.