Playing their second straight game without the NBA's reigning defensive player of the year, Gasol, who is expected to be lost for 3-4 weeks with a sprained MCL in his left knee, the Grizzlies built a big lead by overpowering Boston in the paint and hung on late.
"We're playing well. Everyone's contributing. We've got to continue to do that," Bayless said of the team's effort without Gasol. "We still have Zach and Zach's a premier big man in the league. We've got to continue to get him the ball and he's capable of doing great things."
Kosta Koufos had 13 rebounds and seven points, starting at center in Gasol's absence. Randolph added seven boards.
"Obviously, we're going to have to do it by committee and his presence can't be filled by one guy," former Celtic Allen said. "We're going to have to do it together. Guys went down in previous seasons. We've got to understand there's a lot of games left."
The Grizzlies grabbed the lead in the game's opening minutes and never trailed the rest of the way -- though Boston made a late charge in the last 2 minutes.
The Celtics trailed 90-77 with just under 2 minutes left before Sullinger's late scoring barrage.
It came after Boston finally figured out how to guard the paint better.
"That's why it's a game of adjusting, changing," Celtics coach Brad Stevens said. "If you look at the game, you give yourself a chance to win. We were never quite back in the game."
Memphis' five-game road winning streak is two off the club record set from Feb. 17-March 10, 2010.
"It always feels good coming back to Boston and getting a win for me personally," said Allen, a member of Boston's 2008 NBA champions.
Boston had won its last two games, both on the road.
Memphis opened a double-digit lead late in the first quarter en route to a 49-36 halftime edge.
"They just came out aggressively and our intensity wasn't there," Green said. "We allowed them to put us on our heels and that's how they got their early lead."
Grizzlies guard Mike Miller and a few of his teammates came out to warm up for the second half and there were no basketballs on the court. They had to stand around and wait a few minutes till some were brought out.
It didn't matter because they were getting enough easy shots to keep fending off any charge the Celtics made.
Boston cut its deficit to nine points three times in the third, but the Grizzlies kept going inside against the Celtics' interior defense. Seven of Memphis' nine baskets in the quarter came from inside the lane.
Miller and Bayless each hit 3-pointers in the fourth and Memphis never allowed Boston to get close until Sullinger hit a pair of late 3-pointers and scored eight straight points in the closing 2 minutes.
Bradley's 3 with 14.4 seconds left cut Indiana's lead to 96-93. Bayless made two free throws with 13 seconds remaining to seal it.
In the first half, the Grizzlies scored the final 11 points of the first quarter, taking a 27-13 lead at the break. Boston hit only 5 of 18 shots from the field in the quarter. Bayless had three points and Miller nailed a 3 during the spree. Memphis' first eight baskets in the game came from layups or very short jumpers.
Bayless scored seven points as Memphis had 11 of the first 17 points in the second, pushing its lead to 38-19 midway into the quarter.
Bradley nailed a 3 from the left corner for Boston, slicing the gap to 45-34, but the Celtics never narrowed it into single digits in the opening half.
Celtics guard Courtney Lee sprained his left knee in the second half and didn't return. ... Boston F Kelly Olynyk missed his third straight with a sprained right ankle. ... Stevens said before the game that the Celtics would have a "small" inside lineup with the 7-foot Olynyk out. It hurt them in the opening quarter. ... Boston's Green was handed a microphone and spoke to the crowd at center court before the tip-off, wishing them a Happy Thanksgiving. ... Memphis also beat Boston at home on Nov. 4.