Stauffer tossed three simulated innings before the Padres faced the Nationals. He sat down between innings in order to simulate what he would do if he were pitching in a game.
He also got to face Quentin, who is working his way back from arthroscopic surgery on his right knee on March 19.
Stauffer, on the disabled list since April 5 with a strained right elbow, will throw a normal side session on Thursday at Petco Park. If he comes out of that fine, he'll make a rehabilitation appearance with Class A Lake Elsinore.
"He's still getting the rust out a little today," Padres manager Bud Black said of Stauffer. "... His arm feels better than anytime this spring. He feels like he's throwing the ball like he should. With rest, he feels he is in a good spot."
There's still no projected date for the start of Quentin's rehabilitation appearance, Black said.
"He still has some things he needs to do to go play in a game," Black said. "Run the bases, sliding ... he's still got to pass those. We haven't challenged him to the point of high exertion yet."