Tepesch threw 3 1/3 scoreless innings on Monday -- his first appearance since a sore right elbow landed him on the DL July 6.
The 24-year old is 4-6 with a 4.67 ERA this season and although he will start Sunday's series finale against the Angels, the Rangers will skip the fifth-starter spot the next time it comes up.
"He's starting Sunday and then we'll just leave it at the for now," Washington said.
The Rangers moved up Yu Darvish's next start from Tuesday to Monday and bumped Martin Perez from Monday to Tuesday, allowing the club to go with Saturday's starter Derek Holland, Darvish and Perez, in order, Sept. 13-15 when the A's visit Rangers Ballpark.
The decision for Sunday's game came down to Tepesch or Travis Blackley.
While Blackley did not get the nod, Washington said it was nothing against the left-hander and that he still is valuable in the bullpen.
"Blackley still gives us options," Washington said.
William Boor is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.