The winners got a three-point basket by Larry Bird and a basket off an offensive rebound from Bill Walton in the final 2:30 of play. Rodney McCray's tip-in was the Rockets' only score in the final 4:21.
Houston had the ball with 25 seconds remaining, but Ralph Sampson's pass was tipped away by Boston's Kevin McHale and recovered by Dennis Johnson with 11 seconds left. The Celtics then ran out the clock.
That play, along with Walton's score, typified the game, a bruising affair that was easily the best played and most dramatic of the series thus far.
There was Johnson making a three-point field goal with the shot clock down to one second and a hand in his face. That sight was topped by Sampson dunking and nearly throwing the Celtics' Danny Ainge through the goal too when the guard tried to block the shot.
Robert Parish and Johnson led Boston with 22 points each. Bird just missed a triple double, scoring 21 points with 10 assists and nine rebounds.
Akeem Olajuwon had 20 points and 14 rebounds for the Rockets. Sampson's game-ending miscue marred what could have been a brilliant night. The 7-foot-4 center/forward led his team with 25 points and had nine assists and seven rebounds.
"I just wanted to set a pick for someone," said Sampson. "I wound up out front with the basketball. I tried to give it up but then I guess McHale got his hand in there."
Game 5 will be played here Thursday and should the Celtics emerge with their 16th league championship, all of the Rockets will have cause to reflect upon what could have been had they won tonight.
"This should be a happy, joyous locker room but we lost the game," said guard Robert Reid. "We realize that we were in it but the game just slipped out of our hands."
Out of their hands, off of the rim -- in the closing minutes of the game it didn't matter as for the first time in three weeks the Rockets failed to come through in the clutch.
"We just missed the shots we wanted to take," said guard Mitchell Wiggins. "I don't know if it was their defense or what, but we had some troubles in the end."
The score was tied after the first period, Houston led by a point at halftime. The Celtics moved ahead by one after the third quarter, and in the final 12 minutes neither team led by more than a basket until Bird's three-pointer with 2:26 left, a shot that was made after a pass from Walton.
"The moment I threw it to Larry I knew it was down," Walton said.
"It wasn't a designed play, it was just what happened out there," said Bird. "We moved the ball around and it swung to me. The shot clock was running down and I had to shoot it."
Bird was nine for 17 from the field, a far better effort than his 10-for-26 mark in Game 3, when much was made of the defensive job turned in by Reid.
The Rockets began tonight's game with Reid trying to contain the three-time NBA most valuable player, but Bird hit his first two shots.
"Forget Bird," snapped Reid. "We came out to play, they came out to play. There's no more one-on-one things now. Our team lost a game, their team won a game."
For much of the night it appeared that Houston would even the series. The pace of the game was decidedly uptempo, something the Rockets had struggled to attain in the previous three contests. Although Olajuwon stuggled with his shot (he made eight of 21 from the field), he was effective on the boards and Sampson was overpowering. Add in Jim Petersen's nine rebounds and it seemed like a return trip to Boston to end the series was a fait accompli.
Then again, the Rockets were playing the Boston Celtics, winners of 30 of their preceding 33 games. Unlike their 106-104 Game 3 loss last Sunday when the team seemed to come unglued in the closing minutes, Boston began to grind. Each shot became more highly contested; on each rebound more and more bodies collided.
"Everybody just got down and got dirty," said McHale, who had 19 points and nine rebounds. "Larry and Robert and I don't jump that high like those guys do, but we get the job done."
The best leap of all for the team was provided by Walton with just over a minute left when he followed up a Johnson miss, banking the ball in over a maze of hands and making a genius of Coach K.C. Jones, who had inserted him into the game two minutes earlier after Parish had missed the Celtics' previous two field goal attempts.
"I was running out of gas with two minutes left, everyone could see that," said Parish. "I was running on fumes. I was so tired I almost broke the rim [with his shots]."
"Great move on my part," Jones joked. "I had no second thoughts about putting Bill into the game. He knows where the offensive rebounds are."
And now, the 12-year veteran is just a victory away from his second NBA championship, almost a decade after he led the 1976-77 Portland Trail Blazers to the title.
"After nine years it's very nice to be back," Walton said. "Last year I was watching the finals at home in San Diego, but I'm glad to be a part of it this year."
So are the Celtics.