The Cubs, who were limited to two hits and had eight strikeouts through six innings, exploded with five straight hits to open the seventh and break open the ballgame.
Chicago leads 5-1 after eight innings.
Anthony Rizzo led off with a ground-ball single to right that eluded both first baseman Jose Martinez and second baseman Matt Carpenter. Ben Zobrist followed with a hard-hit single to right and then Addison Russell 's homered down the left-field line to put the visitors on to 3-0.
After a Javier Baez doubled to left-center, former Cardinal Jason Heyward doubled inside the first-base bag for a 4-0 lead.