Seattle has won three of its last four games, and Lewis has been the team's leading scorer in all of those games. The 6-10 forward hit a jumper with 3:29 left to give the Sonics their biggest lead, 94-80.
The Rockets battled back, putting together a 13-3 surge during the next three minutes. Glen Rice nailed a three-pointer with 28 seconds to play as Houston pulled within 97-93. Lewis made a free throw before Allen hit a pair from the line with six seconds remaining to seal the victory.
"We know we need to scrap in order to have an opportunity to win," said Seattle Coach Nate McMillan. "These guys came out and scrapped tonight. (The Rockets) are a tough team to defend with all the players that they have that can isolate you."
Point guards Brent Barry and Kevin Ollie were charged with containing the dynamic backcourt tandem of Francis and Mobley.
Francis collected 23 points, nine boards, and 10 assists, but the All-Star was held without a basket in the fourth as the Rockets had their season-high five-game winning streak snapped and fell into a tie with the Phoenix Suns for the final playoff spot in the Western Conference.
"We made it tough for Steve going down the middle to penetrate," Allen said. "I think we had them frustrated offensively."
Francis and Mobley combined to commit eight turnovers.
"I think the unforced turnovers we had, the mental mistakes, the throwing the ball away at inopportune times really cost us," said Houston assistant coach Larry Smith.
The Rockets made the trip to Seattle without Coach Rudy Tomjanovich, who was diagnosed with a superficial bladder tumor that will not require surgery.
"What coach went through had an effect on us," Francis said. "I know coach and I know how he is. He would want guys focusing on basketball today."
Barry and Ollie also managed to push the offense for Seattle.
Barry had eight assists, while Ollie scored 13 points on 6-of-8 shooting and added six assists in 26 minutes off the bench.