Memphis used a steady diet of Randolph and Marc Gasol to defeat Oklahoma City 114-101.
Randolph had a playoff career-high 34 points with 10 rebounds. Gasol also chipped in 20 points while grabbing 13 rebounds.
Oklahoma City made runs in the game, but Memphis hit key shots to turn the Thunder back each time.
At times, the Thunder looked lethargic, getting beat to loose ball after loose ball.
The Grizzlies also had 11 steals and at one point led by as many as 17 points. The Oklahoma City Thunder gave up 52 points in the paint and turned the ball over 18 times.
Kevin Durant and Russell Westbrook combined for 62 points, but struggled to score baskets late in the game.
James Harden—who had been key for the Thunder—was held to five points on two-for-five shooting and one-for-three from the three-point line.
If the Thunder are to come back and win this series, they will need to get better production from James Harden and the Oklahoma City bench.
Will the Thunder win game 2?
The Memphis Grizzlies got plenty of help from their bench, who outscored the Thunder's reserves 27-16. As of late, Memphis has played great on both ends of the floor, holding Oklahoma City to 44 percent shooting from the floor while shooting almost 50 percent offensively.
For a player who's played for four different teams in 10 years, Randolph has played better than one might expect.
After the game, Durant called him the best power forward in the game. ''I've got to agree with him," Randolph said with a smile.
Randolph is smiling because he knows if Oklahoma City can't figure out a way to contain him and Gasol in the paint, they will have to come to Memphis down 2-0—which would put the Thunder in a whole lot of trouble.