BOSTON (AP) — Kevin Garnett had 28 points and 14 rebounds, hitting a jumper to give Boston the lead with 31 seconds left, and the Celtics beat the Atlanta Hawks 83-80 in Game 6 on Thursday night to win their first-round playoff series and advance to the Eastern Conference semifinals for the fifth straight year.

The Celtics will play the Philadelphia 76ers, who eliminated East No. 1 seed Chicago in six games with a 79-78 victory earlier Thursday.

Garnett topped his regular-season high of 25 points and had five blocks and three steals for Boston, which has won at least one playoff series every year since the new Big 3 was assembled. Paul Pierce had 18 points despite playing with a sprained medial collateral ligament in his left knee, and Rajon Rondo had 14 points and eight assists.

Josh Smith had 19 points and nine rebounds for Atlanta, which failed to advance in the playoffs for the first time in four years. Joe Johnson had 17 points, Marvin Williams added 16 and eight rebounds and Al Horford had 15 points and nine rebounds.

But Horford missed the first of two foul shots with 2.3 seconds left after he was tackled by Marquis Daniels to avoid an easy dunk that would have tied the game. After he made the second, the Celtics got the ball to Pierce, he was fouled and made both free throws.

The Celtics will open the second round against Philadelphia in Boston on Saturday night. The crowd burst into a cheer — even the Celtics players were checking it out — near the end of the third quarter when the final play of the Sixers-Bulls game was shown on the scoreboard.

Instead of having to face Chicago on the road — even without injured star Derrick Rose — the Celtics will have home-court advantage against eighth-seeded Philadelphia.

The Hawks went 5 minutes without scoring early in the fourth quarter as the Celtics turned a two-point game into a 74-65 lead. But Atlanta scored 10 of the next 12 points, with Horford scoring the last three baskets, making it a one-point game on an alley-oop pass from Smith with 3:52 left.

Smith faked at the top of the key and went right down the lane for a dunk that gave Atlanta its first lead of the second half, 77-76. Horford drove to the basket to give the Hawks a three-point lead.

Atlanta still led 79-78 when Garnett made a turnaround jumper in the lane over Smith to put Boston ahead by one. Smith missed a long rainbow jumper and Ray Allen got the rebound with 10 seconds left, but he made only one of two free throws.

With 10 seconds left, Johnson drove to the basket but Pierce blocked his shot and Garnett tipped it out of bounds with 3.1 seconds left. The Hawks got the ball in to Horford in the lane but as he went up for the dunk or layup Daniels, who played just one minute in the game, wrapped him up and kept him from scoring.

The first foul shot went off the rim, costing Atlanta a chance to tie it.

Notes: Pierce injured the knee during Sunday morning’s shootaround and hurt it again when he tried to get around a screen set by Smith during Game 4 that night. … Doc Rivers became just the third coach in Celtics’ history to record 50 postseason victories, joining Red Auerbach (90) and K.C. Jones (65) . New England Patriots defensive lineman Vince Wilfork was at the game. … The Hawks lost to the Celtics in the first round of the 2008 playoffs, a series that went seven games. Boston went on to win its NBA-record 17th championship. … Allen, the NBA’s all-time 3-point leader, was 1 for 7 from beyond the arc. … The Hawks are 1-11 in playoff series against Boston. They last beat the Celtics as the St. Louis Hawks to win the 1958 NBA title. … Rondo had three assists and two baskets during a 16-0 run in the second quarter. Pierce, who came back off the bench in the middle of the run, had five points and a steal over the span of 4 minutes.