After more than a week out, the point guard scored 22 points while wearing a protective mask to help the Grizzlies level their Western Conference semi-final playoff series.
Memphis looked the sharper of the two sides from the outset, with nine points from Conley in the opening 12 minutes immediately putting them six points up.
Leandro Barbaso made a series of shots at the start of the second as the Warriors pushed to get back into the game, but Conley and Tony Allen made sure that the Grizzlies remained in control.
Newly-crowned league MVP Stephen Curry was unable to find his rhythm, finishing with 19 points, while late pushes from Draymond Green and Klay Thompson could only get the home side within seven in the fourth quarter.
The sides meet again on Saturday at FedExForum in Memphis.