The Cardinals dropped their third in a row, having started the night four games behind Pittsburgh in the National League Central.
Rusin (2-1) made his fifth start of the season and he held the Cardinals without a run despite giving up seven hits in six innings. He walked two and struck out five.
St. Louis did not manage a hit against the Chicago bull pen and Kevin Gregg finished off the shutout by collecting his 24th save.
Chicago had runners on first and second with two away in the seventh inning of a scoreless contest when Junior Lake singled in the go-ahead run. Rizzo soon followed with his two-run base hit.
All three runs were charged to starter Lance Lynn (13-6), who allowed only three hits over 6 2/3 innings but got into trouble with five walks.