Crichton was 1-0 with a 3.86 ERA in two relief appearances at Norfolk. Drafted in 2013, he has yet to pitch at the major league level.
Drake had no record and an 8.10 ERA in three games with Baltimore this season, his third with the Orioles.
Also Thursday, Orioles manager Buck Showalter confirmed that right-hander Alec Asher will be promoted from Triple-A Norfolk to start against the Blue Jays on Saturday. Asher, who joined the team in Toronto Thursday, is 2-7 with a 5.88 ERA in 12 career starts with Philadelphia in 2015 and 2016.
Thanks to three off days so far, Saturday marks the first time this season that Baltimore needs a fifth starter.