Odom and West "have so much pressure on them, but they've responded," said Mavericks guard Jason Terry, who added 12 points. "Every time they've been asked to step up in their roles, both of them came up big."
Shawn Marion had 14 points and a season-high 12 rebounds for the Mavs, who closed out a four-game road trip with a second straight close win after a pair of narrow losses to the Clippers and Lakers in Los Angeles.
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"We had to get productivity from a lot of different guys. ... It's a great win," Mavs coach Rick Carlisle said. "I'm also very proud of the way after the first two losses on the trip we bounced back and really gutted two games out, which is not easy to do."
The foul gave Jack two free throws. He missed the second on purpose, but could not convert a quick putback for the tie, and the Hornets fell for the 13th time in 14 games.
"We're just not closing out games the way we know that we can," said Trevor Ariza, who had 12 points. "That's the story of our season so far."
Emeka Okafor tied a season high with 16 points and grabbed a season-best 17 rebounds for New Orleans. Carl Landry added 19 points, but after hitting his first five free throws, missed four of eight in the fourth quarter with the outcome potentially in the balance. Jack scored 12 points.
Odom, acquired in a preseason trade with the Lakers, started for Nowitzki, who is expected to sit out at least three more games while working on his conditioning and getting treatment for his sore right knee.
Odom was only 6 of 14 from the field and missed four of five 3-point shots, but his baskets were timely.
"The ball found him two or three times and he made important plays for us," Carlisle said. "He's getting a better feel for how to play with our guys and tonight was a good indication of that."
Brendan Haywood grabbed 10 rebounds to help the Mavs win a second straight game.
The Hornets had several chances to tie it in the final minutes, starting with Ariza's missed jumper, after which Kidd grabbed the long rebound while sprinting up court and whipped a pass to Terry for a transition jumper to make it 79-75.
After Okafor cut it to 79-77 and Terry missed a 3, Landry was fouled inside, but made only one free throw to make it 79-78.
Another Terry jumper rimmed out, but the Hornets could not take advantage as Ariza missed an off-balance fade. The Mavericks secured the rebound with just over 25 seconds left and the Hornets had to foul.
After West's free throws, Landry scored inside to cut it to 81-80 with 6.7 seconds left.
Terry was fouled after grabbing the inbound pass and hit both free throws to set up the final sequence.
For the Hornets, it was only the latest instance in which scrappy defense kept them close, only for them to come up short on the offensive end while explosive scorer Eric Gordon missed his 14th game of the season with a bruised right knee.
The Hornets finished shooting 37.2 percent (29 of 78), while Dallas shot 40.5 percent (32 of 79) and outrebounded New Orleans 48-41.
"Our defense is holding teams in the 80s, which is what we like to do," Hornets coach Monty Williams said. "Now our guys have to go out there and have some fun and score the ball and trust the offense a bit."
The game was tied at 41 at halftime, but Dallas opened the third quarter with a 12-0 run during which Odom and West each scored once inside and hit 3s. New Orleans, which made only two of its first 12 shots in the period, struggled to chip away, and Dallas held a 64-53 lead at the end of three quarters.
New Orleans briefly seized control early in the fourth, using a 9-0 spurt highlighted by Greivis Vaquez's three-point play to pull to 66-64.
Odom ended New Orleans' surge with a layup and two free throws, and Marion bounced in a short floater soon after to make it 73-66 and give the Mavs just enough of a cushion to hold on during the final minutes.
- Both teams shot poorly from 3-point range, with Dallas going 4 of 26 and New Orleans 2 of 19.
- Okafor's double-double was his fifth this season.
- The Mavs won one earlier meeting on Jan. 7 in Dallas.
- The Mavs are 2-3 in games decided by three points or less.