After trailing by 17 early in the third quarter, the Bulls cut it to five early in the fourth quarter, but Memphis quickly answered. Allen made a pair of free throws and Mike Conley had a steal and layup to make it 64-55 with 9:30 left before the Bulls rallied.
"In the overtime, we moved the ball better. We created some open shots and we kept attacking the paint," Gasol said. "I think they got too many easy buckets and that's why they got back in the game. Too many of those."
Memphis has won two straight after dropping three in a row.
Rudy Gay finished with 16 points and Conley had 13 points and nine assists.
Trailing 30-25 midway through the second quarter, the Grizzlies scored 13 unanswered points to take a 38-30 lead with 1:57 left in the half. Gay scored six straight points in the span.
Memphis led 44-34 at the half. Conley scored 10 points in the half and Gasol had nine. Boozer and Noah led the Bulls with 10 points apiece. Chicago was just 5-for-18 shooting in the second quarter and committed six turnovers.
"In the second quarter we got in a big hole," Thibodeau said. "That went into the third quarter and we could not get organized. The group that went in there battled back and we wanted to ride it to see if we could climb back into it."
After Boozer's basket opened up the third quarter, Allen capped off an 8-0 run with a dunk to extend the lead to 52-36. Gay's jumper gave Memphis a 54-37 lead, its largest of the game.
Randolph, who missed Friday's win over Sacramento with a sore back, played 41 minutes.
"He got all of his work done without having to dominate the ball. He just did it all with dirty work. Offensive and defensive glass," said Conley.
Deng, averaging a team-high 17.4 points, tried to play through a sore right hamstring in Friday's overtime win at Boston but scored a season-low three points on 1-of-6 shooting before aggravating the injury and exiting late in the third quarter.
NOTES: The Grizzlies swept the season series. ... Deng is listed day-to-day and there are no plans for an MRI.