De La Rosa had thrown 7 1/3 scoreless innings in his previous start, a road victory over the Dodgers.
Rusin, 28, was claimed off waivers from the Cubs at the end of last season. The lefty is 3-2 with a 6.29 ERA in seven games, including six starts, at Albuquerque this season. Colorado called Rusin up as its allotted 26th active player for a May 6 doubleheader, but he did not appear.
With the Cubs from 2012-14, Rusin was 4-9 with a 4.97 ERA in 24 games, including 20 starts.
To clear a roster spot for Rusin, the Rockies optioned left-hander Yohan Flande (7.