"We've got confidence in Dwight to make those free throws when they start doing that, so I thought it was a real good win for us," teammate Chandler Parsons said. "But it wasn't perfect."
As they fouled Howard repeatedly, the Celtics trimmed a 19-point deficit to seven in the fourth period before going dry in the final minutes.
"I said (on TV) just now, I would probably support a change in that, that wouldn't allow that, would call it intentional or whatever you want to call it, call it like it would be called in the last 2 minutes," Boston coach Brad Stevens said. "To his credit, he made one almost -- maybe every time up to the foul line."
Jeremy Lin added 16 points and nine assists for Houston. James Harden scored 16 and Parsons added 14 after missing three games with a knee injury.
Parsons is having a breakout season, averaging 17.5 points (on 51.7 percent shooting) and 5.4 rebounds. He said his knee "was really good tonight. I thought it was going to be a lot more sore."
Avery Bradley had 24 points for the Celtics, on their longest losing streak since dropping a franchise-record 18 straight games in 2007 -- the season before they traded for Kevin Garnett and Ray Allen to join Paul Pierce as the Big Three.
"It's hard to go through," Stevens said. "It's unenjoyable to go through. But that doesn't mean there's no growth."
Houston outscored Boston 65-38 in the second and third quarters. Howard had 12 third-quarter points as the Rockets expanded a 52-43 halftime lead to 84-65 by the end of the period.
"(Bayless) gave us a chance, just as that whole second unit did," Stevens said. "Some of those guys haven't played that much."
But the Celtics were unable to complete the comeback and Houston held on.
"We are getting a lot of experience on that, getting a lead and then giving it up," Rockets coach Kevin McHale said. "So we are getting better at that."
Houston blew a 25-point lead against the Wizards before rallying to win Saturday.
"It seemed we played with more poise in the fourth quarter than we did against Washington," Lin said.
Bradley had 14 first-quarter points, including two 3-pointers, as the Celtics opened a 27-19 lead and held the Rockets to 29 percent shooting.
Houston's second unit made some quick inroads against Boston's reserves in the second quarter, led by forwards Omri Casspi (12 points) and Parsons. The Rockets' starters re-entered with the score tied at 35 and took off on a 17-8 run to build a 52-43 halftime lead.
Stevens said there is "nothing concrete" on a return date for rehabbing All-Star guard Rajon Rondo, but allowed that it would be "sooner rather than later." Speculation has ranged from Friday against the Lakers to after the All-Star break. ... The Rockets welcomed Parsons back but are still missing center Omer Asik (bruised thigh) and guard Patrick Beverley (broken hand). ... The Rockets lost their two previous visits to Boston. ... Bass was scratched from the starting lineup in favor of Jared Sullinger.
MVP: Dwight Howard scored 32 points and grabbed 11 rebounds. He was absolutely dominant against Boston's feeble frontline, aside from a painful Hack-a-Howard excursion down the stretch. He crushed the Celtics on both ends of the floor.
X factor: It came in a losing effort, but Jerryd Bayless had his Celtics coming-out moment in the fourth quarter, scoring 15 points on a combination of pull-up jumpers and impressive drives to the basket.
That was ... wasted: Avery Bradley was phenomenal in a losing effort, with 24 points (14 in the first quarter). Nearly all of them coming on midrange pull-up jumpers and spot-up looks from the corner. His defense was even better, holding James Harden to 16 points on 18 shots.