West highlighted a 27-point outing by muscling inside for a crucial offensive rebound and launching himself back up through three defenders for a slam dunk with 1:51 left.
He followed that with two clutch free throws to help New Orleans pull away for a 102-94 victory on Sunday night.
Hornets coach Jeff Bower called West's rebound of Emeka Okafor's miss and follow-up dunk "a key play that put the game away."
West said he thought Okafor had "a good look at the basket."
"I just wanted to be there to give him some support," West continued, adding that the Rockets are "really active with their hands, getting their hands on balls, so I just knew I had to go up really strong and just try to finish."
Hornets rookie point guard Darren Collison added 26 points, the fifth straight game he's had 24 or more. His driving floater with 34.6 seconds left put New Orleans up 96-89. He added four free throws and converted a steal into a fast-break layup in the final half-minute to close out a performance in which he also had nine assists.
"I'm just trying to attack as much as I can," Collison said. "Whatever it takes to win games. If I have to use my speed to get inside the paint -- my teammates are all over me talking about trying to use my speed."
Morris Peterson scored 15 points for the Hornets, who led by as many as 17 but found themselves clinging to a two-point lead with 2:16 left before West turned the tide.
Rookie forward Chase Budinger scored 18 points and Aaron Brooks added 15 for the Rockets, who have dropped two straight since they were involved in a three-team, nine-player deal at the trade deadline last week.
Houston was plagued by poor shooting much of the game. Early in the fourth quarter, the Rockets were at 36.8 percent (28-of-76), including 5-of-21 from 3-point range.
Houston made 12 of its last 16 shots, including two of four 3s, but found its range too late.
"We just have to come together as a team and understand what the strengths are of each guy and get it turned around," coach Rick Adelman said. "Offensively we were very impatient."
Kevin Martin, one of the Rockets' new players, had 13 points, while Louis Scola added 12 points and 11 rebounds.
"It's like starting over," Budinger said. "We have new faces on the team and we are just trying to get used to one another. ... The next few days are going to be very important for us."
The Hornets led 74-57 on Stojakovic's jumper in the last minute of the third quarter. Then Collison, who had five turnovers in the third period, turned the ball over twice in the final seconds of the quarter, leading to a putback and a 3, both by Budinger, who got the second shot off with 0.1 seconds on the clock to pull the Rockets to 74-62 heading into the fourth quarter.
Budinger's baskets turned out to be the beginning of a 13-3 run that included six points by Martin, pulling Houston to 77-70.
New Orleans' lead was back to 89-79 after Collison's driving floater off the glass, but Budinger hit a 3 on the other end, igniting a 9-1 Houston run that cut it to 90-88 on Jared Jeffries' inside basket with 2:16 to go.
West's final four points made it 94-88 with 1:26 left and the Hornets held on from there.
New Orleans took its first double-digit lead in the second quarter and went up 47-31 when Julian Wright threw down Thornton's alley-oop lob.
Houston responded with eight straight points highlighted by Shane Battier's 3, then Thornton hit his second 3 of the quarter to put New Orleans up 50-39 at halftime.
Okafor blocked five shots in the first quarter. He finished with six blocks to go with 11 rebounds. ... Collison came in averaging the most assists (8.2) in games started by rookies. ... Thornton and Houston reserve guard Garrett Temple, teammates at LSU last season, guarded each other at times. ... New Orleans is 5-5 since All-Star point guard Chris Paul went out for surgery on a meniscus tear in his left knee.