Klay Thompson hit a clutch 3-pointer with 37 seconds remaining to put the Warriors up by one and keep it that way.
Stephen Curry blocked Ja Morant on the other end and Jordan Poole secured the rebound.
Thompson missed two critical free throws late. The Grizzlies called a timeout after winning a jump ball with 3.6 seconds remaining.
Morant tried to make a lightning-quick driving layup while being defended by both Thompson and Payton, but the ball rolled off the rim as the buzzer sounded.
Draymond Green was ejected late in the second quarter when he was slapped with a flagrant 2 foul after it appeared he pulled on the collar of Brandon Clarke as he went for a basket, dragging the Grizzlies forward to the ground.
With the Warriors holding a 1-0 lead, the series will continue Tuesday with Game 2 in Memphis. Tip-off is scheduled for 6:30 pm PT.
Bay Area News Group’s Madeline Kenney contributed to this report.
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