CHICAGO (AP) -- Never mind the record.
"It's not like we won last year," he said. "We're all pretty much new to the situation."
Paul Pierce scored 17 for Boston, which won its fourth straight and remained six games ahead of Detroit in the conference standings.
Allen was 5-of-7 on 3-pointers, Pierce hit 4 of 5 and Boston made 14 of 25 in all -- one shy of its season-high.
Chicago continued to fade from the playoff picture, despite getting a season-high 24 points from Tyrus Thomas, who started for the injured Drew Gooden, and 19 from Andres Nocioni. With eight games left, the 11th-place Bulls trail Atlanta by five and have to climb over New Jersey and Indiana to make their fourth straight postseason appearance.
"We knew what we were facing [against Boston]," Thomas said. "I think everybody in the room knew what we were facing. They're not the best team in the league, record-wise, for nothing."
Thomas impressed Garnett, who said, "Tyrus has a lot of potential. Obviously, that's no secret. It's all going to be about what he wants to do in this league, if he's able to listen and follow direction and have a work ethic."
Those remain unresolved issues with Thomas, who got suspended by the team for two games after skipping practice last month.
The Celtics were coming off an 88-62 win over Miami in which they held the Heat to 17 field goals, an NBA record since the shot-clock era began in the 1954-55 season. This time, they weren't as sharp.
The Bulls shot 41.7 percent, but a bigger issue for Boston was its inability to hang onto the ball. The Celtics committed 20 turnovers, including a career-high seven by Rajon Rondo.
That allowed Chicago to stay in the game. Even so, the Celtics improved to 32-1 against teams with losing records.
Boston finally broke it open after Kirk Hinrich missed a layup that could have pulled Chicago within six. James Posey and Allen answered with 3-pointers that bumped the lead to 101-87 with 2:50 remaining and put away the Bulls.
"The 3-point line can be very tricky at times," Allen said. "You have so many open looks, and I know I'm capable of making them. Paul knows he's capable of making them, but I think there's a stigma attached when you shoot too many threes -- you're settling. But the way our offense is, we go through the post. Sometimes, that's the shot that's available."
The Bulls collapsed on Garnett, and the Celtics made them pay, stopping several mini-runs with 3-pointers.
"They were obviously trying to control Kevin," coach Doc Rivers said. "By doing that, we swung the ball, made the extra pass, and we found shooters and they made them. That was a big stretch for us."
But a bigger one is about to begin.
A year ago, the Celtics were in the process of finishing with 24 wins and the league's second-worst record. Now, they're gearing up for a run at the title.
"The guys are fun," Garnett said. "The episodes you have are great in basketball, getting to know guys. We disagree, debate, but at the same time we come together."
Rondo had six turnovers against Memphis on Jan. 4. ... Garnett is a leading candidate for MVP, along with Pierce, the Lakers' Kobe Bryant and New Orleans' Chris Paul. But when it comes to Defensive Player of the Year, coach Doc Rivers said it's no contest; Garnett deserves it. "That shouldn't be a debate," said Rivers, whose team was holding opponents to a league-low 41.9 percent from the field entering Tuesday's game. ... The Bulls' Gooden missed his second game with a lower abdominal strain. ... The Bulls recalled G Shannon Brown and F Cedric Simmons from the Iowa Energy of the D-League.