Vicente Padilla pitches Friday against San Francisco, Jon Garland goes on Saturday and Randy Wolf starts the series finale on Sunday.
Wolf gets to pitch on his customary five days' rest after he showed no ill effects from his hyperextended left elbow in pitching seven innings against the Pirates on Tuesday.
Torre said that matchups played into his decision to swap Billingsley with Garland.
Garland is 1-0 with a 3.77 ERA in two career starts against the Giants. Billingsley is 1-2 with a 3.20 ERA in four games against the Giants, but he lasted just four innings and gave up three runs in his most recent start against San Francisco.
"Not a big sampling, but numbers sort of dictate who's better against which team," Torre said. "Garland's had maybe a little more success against the Giants than Bills has."
Billingsley hasn't had success against most teams of late.
Over his last 12 starts, Billingsley's ERA has grown from 3.14 to 3.99, and he's gone 3-6 in those games.
His last five starts since defeating St. Louis on Aug. 18 especially have been problematic. Billingsley is 0-4 with a 5.67 ERA in that span.
Judging by those numbers, an outing against the National League-worst Nationals probably is a welcomed opportunity to post a good outing for Billingsley.
Still, Torre discussed the reasoning behind the move with his pitcher.
"I just told him that we needed to get him straightened out, whether it be a game or an inning or whatever it is," said Torre, who added that Billingsley is an option to come out of the bullpen on Wednesday against Pittsburgh because of Tuesday's 13-inning game.
"We just need him heading in the right direction. And he was fine with it."
But while it might appear that Billingsley is skipping a start, Torre stopped short of using that label.
"I think it's with the choices we have ... we can look at and plan certain things if there's a matchup thing that sort of makes sense," Torre said, referencing the Dodgers' deep staff and the two upcoming days off, beginning with Thursday.
"We certainly don't want to dismiss him because he's too important for us. So we want to get him out there again."
David Ely is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.