Thursday's off-day made the move possible.
Rays manager Joe Maddon explained the rationale behind the move, noting that Cobb has more experience, he has been pitching well, the Yankees are a division rival on a roll and Odorizzi just arrived.
"Everything speaks to [the move]," Maddon said. "It's not a slight to anybody. It's probably the right thing to do. Anybody given the same circumstances or choice [would do the same thing]."
When Maddon first mentioned the possibility that Tampa Bay might alter the rotation, there was reason to believe Roberto Hernandez might be asked to miss a turn based on his two-inning performance against Baltimore on Saturday. But Maddon noted that was never a consideration.
Bill Chastain is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.