Kevin Garnett had 24 points and nine rebounds as 80, at TD Garden.
Rudy Gay had 21 points and seven rebounds to pace Memphis, which wrapped up a three-game road trip with a 1-2 record by dropping its last two contests.
"We didn't get back on defense," said Grizzlies head coach Lionel Hollins. "They had 26 fastbreak point on us and that was huge."
After an 8-2 spurt by the Grizzlies put them up, 12-6, in the first quarter, the Celtics reeled off 10 straight points to jump ahead and held a 24-16 lead after the opening frame.
Wilcox scored his 12 points in just 11 1/2 minutes off the bench, including 10 points in the first quarter.
"I just wanted to come out and be aggressive and just give great energy. And that's what I did," said Wilcox.
Memphis then came out hot in the second, opening the quarter with a 16-3 run that included five consecutive Boston turnovers and eight points by O.J. Mayo to take a 32-27 lead with less than seven minutes to go in the half.
The Celtics, though, responded with their own 16-3 swing to close out the half and owned a 43-35 advantage at the break.
Neither team shot well from long distance in the first half, as Memphis went 1-for-7 from three-point range and Boston connected on 1-of-10 shots from beyond the arc. Both teams also had 10 turnovers apiece in the first 24 minutes.
But Boston found its three-point stroke in the third quarter, converting on 5- of-8 shots from long distance -- three from Allen -- as the Celtics led by no less than five points and by as many as 12 en route to a 69-61 lead at the end of three quarters.
The game was never in doubt in the fourth, with Boston leading by double digits for the majority of the quarter.
Boston improved to 9-6 at home this season while Memphis fell to 5-9 on the road...The Celtics will also host Charlotte and the Los Angeles Lakers in the homestand...Boston recorded its first win of the season against a member of the Western Conference. The Celtics had been 0-4 against Western Conference foes...Pierce sits nine points shy of tying Larry Bird (21,791) for second on Boston's all-time scoring list...Mayo finished with 15 points for the Grizzlies.