Hayes had 11 points and 11 rebounds for the Rockets, who've won three in a row and moved within 1 1/2 games of Memphis in the race for the final playoff spot in the Western Conference.
The Rockets shot well and pulled away in the second quarter, outscoring Boston 34-18. As the deficit widened, the Celtics started losing their poise.
Kevin Garnett and Hayes traded shoves and words, and referee Jason Phillips gave them both technical fouls. Hayes was glad to get one and make a statement that the Rockets weren't going to back down.
"They tried to isolate him on the block, and that was the wrong time to do it," Hayes said. "I had so much adrenaline rushing, I was determined not to let him get a score."
On the next play, Glen Davis fell into the crowd along the baseline after he was pushed by Jordan Hill, then got up yelling and pointing at Hill. The Houston backup forward was called for a personal foul, and Davis got a technical with 2:45 remaining.
"It was just a wild sequence there," Hayes said. "We took the momentum. They tried their best to be aggressive. We fought them right back."
A minute later, Delonte West was whistled for a flagrant foul when he hammered Hill under the Rockets' basket.
Houston took advantage of Boston's outbursts, hitting all the resulting free throws and extending the lead to 58-37. Kyle Lowry swished another 3-pointer just before the buzzer to put the Rockets ahead 62-40 at the break.
"We were just terrific," Houston coach Rick Adelman said. "That was about as good as we can play at both ends of the court. We were reactive, we really moved the ball well, we were getting good opportunities."
Jeff Green scored 17 points and Davis added 16 for the Celtics, who've lost four of six. Boston slipped a half game behind Chicago for the best record in the East.
Paul Pierce scored 10 points, but went 2 for 10 from the field, and Rajon Rondo had only four points on 2-for-11 shooting. Boston's point total was a season low for a Rockets' opponent.
Coach Doc Rivers rested his starters for the entire fourth quarter, about the only positive thing to come out of the performance.
"I just thought, 'Let's just throw this one away," Rivers said. "This is one of those games where they did everything better. You just go on to the next game."
The Rockets went 7 for 14 from 3-point range and 15 for 15 from the free throw line in the first half. Martin had 19 points and Lowry had 16 in the first half, while the Celtics had no players in double-figures.
"We can't let our offense dictate what our defense does," Garnett said. "We couldn't get stops. It seemed like when they took over the game, they just ran with it."
Patterson slipped inside for a two-handed dunk early in the third quarter, and the Rockets kept control. He slammed home a rebound later in the quarter to make it 81-52.
Houston mustered only 12 points in the final quarter, but still never let the lead dip below 16. The Rockets went 21 for 23 from the free throw line and outrebounded Boston 44-35.
"We knew that they were very physical and they were going to grab and pull and they were going to try and intimidate," Adelman said. "We've got a young group, and all we talked about before the game and at timeouts was that you play through it. I was really pleased with the way our guys approached it."
The Rockets led 28-22 after the first quarter, and reserves Goran Dragic and Brad Miller hit 3s early in the second to push the lead into double digits. Rivers had his starting lineup back in by the midpoint of the second quarter, but Martin's 3 with 4:25 left gave Houston a 47-33 lead.
The Celtics let their frustration boil over after that, and the Rockets were never threatened again.
Rivers said athletic trainer Ed Lacerte will have the final call on when C Shaquille O'Neal returns from a right Achilles' injury that's kept him out since Feb. 4. "He's not playing until the doctors say he can play," Rivers said. ... Rockets F Luis Scola sat out for the fifth straight game with a sore left knee. Adelman expected Scola to return to action next week. ... The Rockets had lost the previous four meetings with the Celtics in Houston.