Anderson (1-0) got his first win in five starts and tamed a Chicago lineup that had 16 runs on 18 hits in the series opener on Friday night. The Cubs managed just six hits on the night, two from Albert Almora Jr., who had four in Friday's win.
Wade Davis pitched the ninth for his ninth save in 10 chances.
Chicago's offense wasn't as potent behind starter Yu Darvish. He started strong but left with two outs in the fifth after allowing five runs on five hits and walking four.
Darvish didn't allow a hit until Arenado's two-out single in the fourth, but the Rockies got to him in the fifth. After a two-out walk to Anderson, DJ LeMahieu had an RBI double and Gerardo Parra followed with a two-run single to give Colorado a 3-2 lead.
Charlie Blackmon walked, Arenado drove in another run with a single and Trevor Story's RBI double made it 5-2 and chased Darvish.
For the second straight night the Cubs grabbed a quick lead. Almora and Javier Baez led off with singles and scored on a double by Wilson Contreras to make it 2-0.
Anderson settled down after that and worked out of trouble in the third. The Cubs had runners at first and third with one out but Anderson got struggling Anthony Rizzo to pop out to second and Contreras to fly out to center.
