Houston improved to 11-2 in play-off elimination games under the coach, Rudy Tomjanovich, with a 96-91 victory in game seven of their Western Conference semi-finals.
The Rockets, who were led by Clyde Drexler's 24 points, including two free throws in the final 20 seconds, will open the conference finals against Utah tonight in Salt Lake City.
The Rockets, slammed in the opening minutes of their two previous losses, charged right at the SuperSonics and chiseled out a 55-50 half-time lead that was hard-fought all the way. Houston finally got a little breathing space in the third quarter but not much.
The SuperSonics scored the first six points of the third quarter to regain the lead at 56-55 but it was short-lived as the Rockets scored seven straight points on baskets by Barkley, Drexler and Olajuwon and a free throw by Drexler to open the biggest lead of the game, 62-56 with 7:58 left in the third quarter.
The Sonics didn't score over the final 3:02 of the third quarter and the Rockets took a 74-67 lead into the fourth quarter.
Houston once again had first-quarter problems hitting their layups and they were outrebounded 13-5 in the first period. Still, they at least did not fall behind 16-2 and 15-5 as they did to start their previous two games.
The Rockets led 88-74 with 3:58 to play as the Sonics missed 12 straight shots and went 6:14 without a field goal. The Sonics' only points during that span that started with 3:02 to play in the third quarter, was a free throw by Shawn Kemp with 9:11 left in the game.
The Sonics, the defending Western Conference champions and the team that beat the two-time defending NBA champion Rockets in this same round last season, were not ready yet to concede victory. Hersey Hawkins had half the points as the Sonics went on a 12-1 run that cut Houston's lead to 89-86 with 1:32 to play.
Matt Maloney hit a three-pointer - his only points of the second half - with 1:17 to play to give the Rockets a six-point lead. Two free throws by Gary Payton and a basket by Detlef Schrempf with 21 seconds to play had Seattle within 92-90.
Drexler made one free throw with 20 seconds to go and another with 17 seconds left and Hakeem Olajuwon dunked the final basket with 1.4 sec to play.
After Schrempf's basket cut Houston's lead to 92-90, Terry Cummings missed the first of two free throws and Kemp missed a desperate, off-balanced shot as time ticked down and Schrempf then lost it out of bounds.
Payton led the Sonics with 27 points and played 46 minutes and Kemp finished with 21 points and 10 rebounds.
Olajuwon scored 22 points for Houston and had 13 rebounds, while Barkley finished with 20 points and 14 rebounds.