Rudy Gay added 18 for Memphis, while Marc Gasol and O.J. Mayo finished with 10 apiece.
Young, a rookie from Pittsburgh, went 4 of 7 from the field and hit 13 of his 16 free throws in just under 20 minutes.
"As you can see, I'm starting to get more comfortable with the system," Young said after only his second preseason game. "I just need to pick up what coach [Lionel] Hollins is telling me as a whole. I need to learn the plays and make sure I execute the plays right."
Kevin Durant scored 17 for the Oklahoma City, which was playing its preseason opener. D.J. White had 16 for the Thunder, and rookie James Harden finished with 12. Nenad Krstic and Shaun Livingston contributed 10 apiece.
"This was the first game of the preseason," Durant said. "Guys got the jitters off; the butterflies out. I think we played together. We moved the ball, but we had some tough stretches of turning the ball over or not running [the offense].
"I think [the game] was a step forward."
The Grizzlies announced before the game that guard Allen Iverson could miss up to three weeks after an MRI on Wednesday revealed a partial tear of his left hamstring. The injury could jeopardize Iverson's availability for the Oct. 28 season opener against the Detroit Pistons.
"For Allen to go down is really tough on the team, but he's been there for us," point guard Mike Conley said. "He's in here every day trying to get us ready to go."
The teams were tied at 80 with just under 8 minutes left before Memphis went on an 11-3 run to put away the game. Young's steal and dunk made it 91-83.
"I just went out and tried to make the best of my situation," Young said. "Knowing that Allen was hurt didn't change my demeanor one bit. When I get the opportunity, I will showcase my talent."
Both teams played their starters about 10 minutes in the first quarter and let most of them close out the first half. Between those stints, reserves tried to show their value to the teams.
At one point in the second quarter, Oklahoma City's rookies, Harden of Arizona State and B.J. Mullens of Ohio State, were on the floor with the Thunder's core of Durant, Jeff Green and Russell Westbrook.
"Overall, I think I did some pretty good things out there," Harden said. "I tried to help my team out on the defensive end, but I've still got a long way to go."
The Grizzlies, who had 26 assists in Tuesday's loss to the Washington Wizards, weren't passing the ball nearly as much, recording only five assists in the first half. They finished with 18.
Michael Henderson, one of two ex-NBA officials called back as replacements during the current lockout, was part of Wednesday's officiating crew. Henderson was fired by the league in 2005. The other former official brought back as a replacement, Robbie Robinson, worked Memphis' game against Washington on Tuesday night. Thunder coach Scott Brooks said he is not quite ready to announce the team's captains, but he is "pretty close." He plans to select two. "I just want to make sure my choices understand their role," Brooks said. "I take it serious. I've been around some great captains, and I've been around some not-so-great captains." Officials reviewed a play with 10:11 left in the third quarter to determine if Harden's shot was a 3-point attempt when he was fouled by Mike Conley. The initial view was inconclusive, but a second angle showed that it was a 2-point attempt. They also reviewed a play at the end of the quarter to see if a foul on Hasheem Thabeet was called before time expired. They determined the call was made 0.1 seconds left.