Harden made six 3-pointers and scored 40 or more points for the 24th time this season. Houston entered the day in fifth place in the Western Conference standings, a game behind of fourth-place Oklahoma City.
Eric Gordon added 32 points and had eight 3-pointers.
The Celtics did a decent job trying to contain Harden, limiting him to 14-of-31 shooting from the field and nine free throw attempts.
But Boston was inefficient when it had the ball, shooting 48 percent (37 of 77) for the game and 29 percent (8 of 28) from beyond the arc.
The Celtics started the fourth quarter with a 17-6 run to cut what had been a 28-point deficit to 106-96 with 6:08 to play.
Terry Rozier got fouled on a 3-pointer at the five-minute mark, but missed all three free throws.
It was 109-100 when Nene gave Houston a second opportunity after a Gordon miss. It wound up in Harden’s hands and he stepped back and swished his sixth 3 of the game to push the lead back up to 12.
But leading 112-104 Harden fouled out when he was called for an offensive foul with 1:44 left.
The Celtics came up empty on their next trip down the floor and they were forced to foul after failing to corral Austin Rivers‘ miss from deep.
Boston earned its first victory since the All-Star break on Friday night against Washington. But on Sunday the Celtics fell back into many of the same bad habits that had caused them to lose four straight prior to that win over the Wizards.
Things don’t get any easier for Boston, which plays its next four on the road. The trip out West begins with a matchup against Golden State and ends with games against the Lakers and Clippers.
Rockets: Iman Shumpert missed his second straight game with a sore right calf
Celtics: Shot 1 for 13 from 3-point line in the first half.
Houston was the more aggressive team on both ends from the outset and led 65-43 at the half. Harden (23 points) and Gordon (20 points) matched the Celtics’ output by themselves in the opening 24 minutes.
The Celtics were often careless in the half court on offense. They turned it over five times in the five minutes of the game, leading to 10 Rockets’ points.
Boston’s giveaways were exacerbated by its slowness getting back in transition.
Other times the Celtics failed to help out teammates when they were beaten off the dribble, allowing to Rockets — and particularly Harden — to get uncontested layups. Houston scored 16 of its first 31 points in the paint.
Boston hoped to get some defensive help with Aron Baynes returning to action after missing this last 11 games with a left foot contusion. But Harden repeatedly forced the Celtics to switch Baynes onto him on defense. Harden easily drove past the big man for layups on three separate occasions.
When Boston did have the ball, they often settled for jumpers or tried to attack Houston one-on-one.
With the Celtics trailing 53-36 late in the first half Marcus Morris airballed a desperation 3-pointer as the shot clock wound down, prompting a chorus of boos from the home crowd.
Rockets: At Toronto on Tuesday night.
Celtics: At Golden State on Tuesday night.
Source: Fox Sports