It was a first playoff win over Miami for the Nets, who trail the best-of-seven series 2-1.
"We weren't going to panic. We wanted to show them we're not scared of them," veteran Brooklyn forward Paul Pierce, who had 14 points, told reporters.
"Everybody was talking about us getting swept, whispers and stuff, but all they did was hold down home court. It's our job to hold down home court."
Led by guard Joe Johnson, who scored a team-high 19 points, six different players scored in double figures for Brooklyn, who shot 60 percent (15-of-25) from three-point range.
Brooklyn attacked from the outset and made the extra pass, which resulted in open shots, especially from beyond the arc.
The attack was led by point guard Deron Williams, who bounced back from a scoreless Game Two to notch nine points and dish out 11 assists.
"The way they are playing me with two on the ball and coming up at me, I need to make the right plays and get people the ball (and) I think I did that," Williams said.
The Nets also had huge contributions off the bench from forwards Andray Blatche and Mirza Teletovic as Brooklyn had a 40-25 edge in bench points.
"A lot of the threes they made were contested, so you clap your hands and pat them on the back for the ones they made because that's just our scheme," Miami forward LeBron James said.
James came out firing early, scoring 16 points on 6-of-7 shooting from the field in the first quarter. But he was just 2-of-8 the rest of the way en route to a game-high 28 points.
Guard Dwayne Wade had 20 points and forward Chris Bosh 12 for Miami, who swept Charlotte in four games in the first round of the playoffs.
"They played a better game than us, simple as that," Wade said. "It is 2-1 and we have to move on. We have to start preparing for the next one."
Game Four is in Brooklyn on Monday.
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