Rose made two free throws with 2:18 left to give Chicago the lead, then drove past Tony Allen and converted over Marc Gasol with 10.8 seconds remaining to increase the advantage to 97-93. Once again hearing those "MVP!" chants, Rose made the resulting free throw.
"I tried to go hard. Try to get the foul," Rose said. "People play me to my left hand, I'm pretty good going to my left. I was just trying to get contact and I did."
At least one Grizzlies player agreed with the delirious crowd.
"MVP. He's my MVP," said Zach Randolph, who led Memphis with 16 points.
The Grizzlies had one last chance after O.J. Mayo connected from long range and Rose had a 1-for-2 trip at the line, but Mike Conley missed from 3-point range over Joakim Noah as time expired.
Rose finished with 24 points, seven rebounds and seven assists for Chicago, which has won 11 of 12 and 18 of 21. Luol Deng scored 23 and Carlos Boozer added 12 points and nine boards.
The Bulls extended their home winning streak to 14 games and increased their lead in the Eastern Conference to two over Boston, which lost 83-81 to Charlotte.
"There is no space right now," Rose said. "We're just trying to win every game. Even if it's by one or two points, we'll take it."
Gasol had 14 points and 11 rebounds for the Grizzlies, who were coming off a 90-87 win at the Celtics on Wednesday. Allen scored 13 -- all in the first half -- and Conley finished with 11.
Memphis, which normally enjoys an edge inside, was outscored 46-44 in the paint and outrebounded 45-32, including an 18-8 edge on the offensive glass for Chicago.
"They just killed us on the boards," Randolph said. "It was a bad rebounding night for us. They don't happen too often."
Conley's drive with about 6 minutes left gave Memphis an 88-84 lead, but the Grizzlies couldn't hold on. Kyle Korver set up Boozer for a dunk and Deng's rebound tip-in quickly tied it up.
Leon Powe had 11 points and fellow reserve Darrell Arthur finished with 10 for Memphis, which dropped to 22-10 in its past 32 games. The long and athletic Grizzlies are currently in the eighth and final playoff spot in the West.
"This one definitely hurt, we have to claw and scratch to get into that eighth playoff spot," Allen said. "I liked our effort tonight but there are no moral victories."
Allen helped Memphis get off to a nice start, slicing through Chicago's defense for a couple of easy baskets and frustrating the Bulls with his active arms and intensity on defense. He also played to the hostile crowd, yelling after a Grizzlies run and galloping down the court after another basket.
Allen's long jumper with 3:12 left in the second quarter capped a 14-2 run and gave Memphis a 45-37 lead. He went 6-for-7 from the field in the first half.
The Bulls responded with a 12-1 spurt to close the period. Deng had eight points, including two 3-pointers, and Rose threw up a fallaway jumper with 1.4 seconds left to make it 49-46 Chicago at the break.
"We made big plays at the end to win. But throughout the game, I just thought they played harder," Deng said. "They got to the loose balls first. They're a very good team."
Grizzlies F Rudy Gay had season-ending surgery on his partially dislocated left shoulder in Pensacola, Fla. He was hurt Feb. 15 against Philadelphia. ... Rose had his right hand in a bag covered in wax in the locker room before the game, a treatment designed to help loosen his joints. He said he's fine -- he saw teammate C.J. Watson try it a couple months ago and wanted to give it a shot. ... Chicago Bears linebacker Brian Urlacher and defensive end Julius Peppers each got a warm ovation when they were shown on the videoboard on separate occasions.