Ludwick hit a two-run double and Schumaker a two-run homer.
Yadier Molina and Matt Holliday had one RBI apiece, while Khalil Greene's RBI single finished a five-run eighth for the Cardinals, who have won four of five.
Winner Joel Pineiro (10-9) yielded three runs and nine hits in seven innings.
Kyle McClellan earned his second save by retiring the final five batters in order.
Pittsburgh's Steve Pearce hit a two-run homer.
Delwyn Young also drove in a run for the Pirates, who have lost eight in a row.
The losing pitcher was closer Matt Capps (2-7).