Playing without injured defensive leader Kevin Garnett for the seventh consecutive game, the Celtics limited All Star LeBron James to 21 points.
"This is a big win—both teams are playing for first place in the East and home court advantage (in the playoffs)," Pierce told reporters. "They were physical, but we played our game and limited our turnovers."
Boston (49-14) forward Leon Powe had a season-high 20 points and 11 rebounds, while Ray Allen added 17 points.
Point guard Rajon Rondo sustained an ankle injury in the first quarter but returned to the action and contributed six points and 10 assists.
The Cavaliers (48-13) still hold a better winning percentage than the Celtics despite dropping their first game in five.
Mo Williams led the way for Cleveland with 26 points while James finished 5-for-15 shooting from the field.
The game was knotted at 57-57 with 6:56 remaining in the third before the Celtics closed the quarter with a 21-12 run to take a 78-69 advantage.
"No (Kevin Garnett) or with KG they are going to be a great team because they buy into the system," James said.
"A lot of teams can't afford to lose an All-Star but they have two more. They still have two superstars who can keep up the same tempo."
In a rematch of last season's hard fought seven-game Eastern Conference semi-finals series, things became testy in the third quarter.
Boston forward Glen Davis was ejected after committing a foul on Anderson Varejao and players had to be separated.
Cavaliers forward Joe Smith recorded seven points and five rebounds in his debut with the team after being signed following his release by the Oklahoma City Thunder.
The Celtics now lead the season series 2-1 with one final game remaining between the teams on April 12.
