Crain had been on the DL retroactive to June 24 with a right posterior shoulder strain and was expected to possibly return on Sunday, but the White Sox felt confident enough in his recovery to push him up one day.
"It's just one of those that we wanted to get back to normal as quick as possible," manager Robin Ventura said. "He felt fine, so it's time to make the move. Get our guys used to being in there in situations to be ready."
Ventura added that right-hander Gavin Floyd is set to return from the DL on Monday night and start Chicago's series opener against the Twins. Getting Floyd back from his right elbow tendinitis will move the White Sox closer to full strength for the final two-month stretch run.
"We are kind of getting ourselves closer to being back to normal, [in terms] of who we had when we left Spring Training," Ventura said.
As for Omogrosso, who produced a 4.26 ERA over five games since he was called up from Charlotte, a sample of the big league experience leaves him desiring even more.
"I'm on that borderline right now," Omogrosso said. "There are still a lot of aspects I can work on to make myself a better pitcher. Hopefully, once I do that, I can stay up here for a good while."