Scott Feldman, who started the middle game of the Kansas City series, will come back on Friday against Arizona on five days' rest.
"We're going to stay in order," Hinch said. "Everybody will get an extra day, which I'm going to do a lot after these off-days coming up. We'll try to get guys extra rest as much as possible."
The current rotation features lefty starters with the top two ERAs in the American League. Keuchel will take a 2.12 ERA into Sunday's start while Kazmir lowered his ERA to 2.24 with seven shutout innings against the Royals on Friday.
In addition, Keuchel (.203) and Kazmir (.208) rank first and third respectively in opponents' batting average.
• Hinch was pleased to hear about switch-hitting infielder Jed Lowrie's performance on Friday in the second game of Lowrie's injury rehab assignment with Double-A Corpus Christi. Lowrie, working his way back from a ligament tear in his right thumb, went 2-for-3 with a double and an RBI in a start at third base.
"Right-handed [hitting], which is the side of the plate we were most concerned about in adjusting after the injury," Hinch said.
Lowrie was scheduled to play shortstop on Saturday, take Sunday off and play third base again on Monday. He went on the disabled list on April 28.
Robert Falkoff is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.