Both games ended in defeats but New York was hoping to erase those memories when it forged a 76-72 advantage through three quarters.
Allen, however, responded with six quick points early in the fourth and Boston went on a 13-3 run to grab a 101-89 lead with 2:34 remaining.
The Knicks had won six of seven before their latest three-game losing skid, including a 100-88 home victory over the Celtics in their previous meeting on January 4, and were hoping for a repeat performance of that triumph.
They started well enough with Harrington sparking New York early with 17 first-half points, including three three-pointers in the second quarter, before Boston's defense settled in and made things more difficult in the second half.
"We talked more, we switched and didn't allow (Harrington) to get open shots," Pierce said. "I think that's the key. When you give him space and allow him to hit open threes he's tough to guard."
Kevin Garnett had 15 points and 11 rebounds while point guard Rajon Rondo had 12 points and 10 assists for the Celtics, who are trying to avoid falling into a slump after losing to the Lakers.
The last time Boston fell to Los Angeles, 83-92 on Christmas Day, it offset a season-worst 2-7 run.
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