The big drives helped the Cubs win their third straight after dropping eight of 12, and they came before two late delays — for 56 minutes in the top of the seventh inning and for 37 minutes at the start of the ninth.
Soler broke a 1-1 tie with his shot halfway up the video board in left leading off the fourth. Ross added a three-run homer off the Nuveen sign beyond the left-field bleachers in the inning to give the Cubs a 5-1 lead, and Bryant chased Adam Morgan (1-3) with a towering shot to start the fifth.
Lester (5-3) rebounded from his shortest start of the season by giving up two runs — one earned — and six hits while pitching into the seventh.