Baker sat out the first six minutes of the fourth quarter because of foul trouble. After Boston's Antoine Walker tied it at 83, Baker played like an All-Star.
"I had a nice rest and when I came back I wanted to finish the deal," said Baker, who finished with 17 points and eight rebounds. "Fortunately, I was able to make some big baskets."
The Celtics had a chance to tie, but missed a 3-pointer with nine seconds left.
Pierce led the Celtics with 23 points and eight rebounds. Walker added 21 points and eight rebounds for Boston, which is 1-2 on a six-game West Coast trip.
Both teams rebounded with solid performances after one-sided losses Friday night. Seattle was coming off a 118-85 loss to Sacramento, and Boston a 122-100 setback at Golden State.
Celtics coach Rick Pitino was pleased with his team's effort.
"If we can keep building on this, we'll get better and better."
Pierce said his team had plenty of chances.
"We were right there," he said. "We got two layups and a shot to tie the game and none of them dropped. Our mistakes down the stretch cost us."
The Sonics biggest lead in the last five minutes was 89-85, with the Celtics staying close ehind Pierce and Walker.
Down 74-71, the Sonics went on a 12-2 run capped by McCoy's dunk for an 83-76 lead with 7:12 left. McCoy had six points during the spurt and gave the Sonics some toughness under the basket.
Payton scored 15 points during the third period. Anderson's two baskets, including a buzzer-beater from 15 feet, gave Boston a 71-69 lead after three periods.
Boston beat Seattle 111-86 during their first meeting at the Fleet Center on Jan. 21.
The Celtics outscored the Sonics 11-2 over the last 2:56 of the first half for a 49-44 halftime lead. Dana Barros and Pierce made 3-point shots during the spurt.
Seattle had taken a 42-38 lead with a 9-0 run. A blocked shot and assist by Foster and five points by Payton fueled the spurt.
Pierce put on a dazzling all-around performance in the first quarter with six points, three steals and two blocked shots. On successive possessions, Pierce rejected Payton's left-hand layup attempt and a jump shot by Patterson.
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