Akeem Olajuwon scored 12 of his 18 points in the fourth quarter and blocked a key shot late in the game as Houston staved off elimination in a first-round playoff series game at Salt Lake City.
The series switches back to Houston for the deciding game Sunday.
The Rockets took a 94-83 lead with 1:19 left and appeared to have the victory in hand. But Utah's Darrell Griffith hit three straight three-point field goals to close the lead to 94-92 with 48 seconds remaining.
After the teams exchanged baskets, Utah had an opportunity to tie, but rookie John Stockton's layup with two seconds left was blocked by Olajuwon as time ran out.
"As I brought the ball down, I looked for someone to pass the ball off to," Stockton said. "I saw nobody around so I put it up. I'm not going to worry about the shot not going in. My only concern right now is going down to Houston and playing."
Sampson also had 18 points while John Lucas and Lewis Lloyd each scored 15. Rickey Green scored 22 points for the Jazz and Adrian Dantley had 20.
The Jazz hit just 29 percent from the field in the second half, going 11-for-38. Utah's Mark Eaton set a NBA single-game playoff blocked-shot record with 10.