"George has been throwing the ball well down there the last five outings," manager Bruce Bochy said. "He's looked good. He's gone two innings a couple times."
Kontos was acquired from the Yankees before the season for backup catcher Chris Stewart. Kontos had a 2-0 record and a 1.71 ERA in 31 2/3 innings in 23 appearances for Fresno this season.
Edlefsen leaves the Giants with a 4.70 ERA in 15 1/3 innings. The right-hander gave up a walk-off home run to Logan Forsythe in Wednesday's 6-5 loss to the Padres.