Marc Gasol scored 24 points and Zach Randolph added 15 as the visiting Grizzlies out-scored the Thunder 30-19 in the fourth quarter. Game Three is in Memphis on Saturday.
Kevin Durant had 36 points, 11 rebounds and nine assists in another big performance for Oklahoma City. Derek Fisher tallied 19 points and went 4-for-5 from three-point range, but the Thunder were hurt by 21 turnovers.
The Grizzlies took a 92-90 lead when Conley drained a three-pointer with 1:58 to play and he followed that up by knocking down an 18-footer with 1:04 left and a free throw with 29.4 seconds remaining to make it a five-point game.
Randolph hit two free throws and Tony Allen slammed home a dunk to cap a 10-0 run and give Memphis a 99-90 advantage.
Gasol had 17 first-half points as Memphis took a 54-51 lead into the break. Durant scored 13 points in the third quarter as Oklahoma City held the Grizzlies to 15 points and led 74-69 entering the final stanza.
(Editing by John O'Brien)