The Grizzlies threw away a 17-point lead late in the game before Conley led the scoring in overtime to seal a 98-95 victory, giving Memphis a 2-1 lead in the playoff series.
The point guard told reporters: "Obviously, we're happy with the win but disappointed at the way we handled that last quarter.
"We knew they were going to make runs. We knew they'd keep fighting because that's what they do, and it's the playoffs. They're going to make runs. They're going to make plays. They have two of the best players in the league."
The Grizzlies, who are making their fourth straight appearance in the playoffs, face the Thunder again on Saturday.