A win at home was critical for Boston, especially after losing in overtime to Miami on Wednesday. The Celtics still trail 2-1 in the best-of-seven series but could now tie it up in Boston on Sunday.
The raucous crowd energised the Celtics, who surged to a 13-point lead by halftime and a 22-point margin by the end of the third quarter. Center Kevin Garnett top scored with 24 points and captain Paul Pierce had 23 points.
"Kevin does so many little things. He does so many intangibles, he's our best communicator. I could go on and on," Boston guard Rajon Rondo said of his team mate.
Rondo, who played all 53 minutes of Wednesday's overtime loss, chipped in with 21 points and 10 assists, steadying the team in the fourth quarter when Miami mounted an aggressive comeback against the tiring Celtics.
"He stayed with us, stabilised us really," Boston coach Doc Rivers said of Rondo.
The Celtics' tough defense - the decisive factor in their run past Philadelphia and Atlanta to the conference final – was back on track in the win.
"The difference was our defensive energy, which allowed us to run," said Rivers. "We had terrific ball movement for three quarters ... our rebounding was terrific in stretches."
Rivers praised the "phenomenal" effort of his team's second string players, including Marquis Daniels and Keyon Dooling, who each got significant playing time.
"What the second unit did was come in with a defensive energy that just changed the game," Rivers said.
Daniels, who played just 18 seconds in Wednesday's game two, logged more than 17 minutes as a stand-in point guard, adding nine points and five rebounds.
The Heat's Lebron James, in pursuit of his first NBA title, dominated the first quarter and ended up as the game's top scorer with 34 points.
The Heat cut Boston's lead to eight points late in the game, at one point staging an 11-0 run.
"He kept us afloat," team mate Dwyane Wade said of James. "We made a run in the fourth quarter (but) we can't dig that big of a hole for ourselves."
Miami did itself no favours from the penalty line, missing 10 of 20 free throw attempts. James was one of five from the line.
"We know this is a tough place to play but we know we can play a lot better than this," said Miami coach Erik Spoelstra.
"We still have a golden opportunity."