Paul Pierce scored a playoff-high 22 points and Ray Allen hit three 3-pointers in the middle of the third quarter Wednesday night to turn back the Hawks’ last charge, leading Boston to a hard-fought 110-85 victory over Atlanta and giving the Celtics a 3-2 lead in the best-of-seven series.

Kevin Garnett scored 20 and Allen had 19 to put the Celtics one game away from advancing to the second round. Boston got a huge lift from its bench in the second quarter, when Sam Cassell scored nine points and Leon Powe had seven with five rebounds while holding Al Horford to a pair of baskets.

Joe Johnson, who erupted for 35 points in Game 4 — 20 of them in the fourth quarter — scored 21, and Horford had 14 points and 10 rebounds for Atlanta. Mike Bibby continued to struggle in Boston, scoring six while recording one assist for the third straight road game.

The first five games have all gone to the home team, with Game 6 in Atlanta on Friday night. A seventh game, if necessary, would be played in Boston on Sunday, an advantage the Celtics earned with their NBA-best 66-16 record in the regular season.

Boston would like to end it in six and get a break from a physical series that saw another double-technical — when Garnett and Johnson were jawing in the third — and another flagrant foul, when Horford took down Garnett late in the first half.

The top overall seed wasn’t expected to have this much trouble in the first round with an Atlanta team that went 37-45 to grab the final playoff berth in the Eastern Conference. But the Hawks answered two losses in Boston with a pair of victories at home, tying the series 2-2 on Monday night.

Pierce scored 18 in that one, on 5-of-14 shooting, finding out just hours before game time that he had been fined $25,000 by the NBA for a "menacing gesture" — allegedly gang-related — during Game 3. Before Wednesday’s game, he issued a statement denying it was a gang sign.

Then he went out and put his hands to a more useful purpose.

After picking up his fourth foul early in the fourth quarter, Pierce held out a dismissive arm toward coach Doc Rivers as if to say: "Relax."

"I won’t foul out," he mouthed.

But Rivers took him out, anyway.

And the Celtics didn’t need him.

The Celtics took a 58-43 halftime lead, holding Atlanta without a field goal for half of the second quarter before Horford’s putback dunk with 1:05 left. Pierce drove for a layup to start the second half, then Atlanta scored the next 11 points to pull within 60-54.

But Garnett made a turnaround hook shot, then he passed off to Allen to set up a 3-pointer. Pierce drove for another basket and, after Horford’s dunk slowed things down temporarily, Kendrick Perkins answered with a follow dunk that made it 69-56.

After a timeout, Garnett blocked Josh Childress and then Allen hit a 3. Allen threw the ball away and helped the Hawks cut the deficit to 12 points, but then he hit another 3-pointer to give Boston a 75-60 lead.