The Hornets led 62-51 after a basket by Austin Rivers with 2:01 left in the third quarter before the 16-2 spurt by Oklahoma City spanning the third and fourth quarters.
The Hornets regained the lead twice after that, but a 3-pointer by Martin put the Thunder ahead for good at 73-72 with 6:20 left. Still, Oklahoma City struggled to pull away.
A three-point play by Durant with 1:12 left pushed the Thunder's lead to 89-84, but Anthony Davis made 1 of 2 free throws with 18.5 seconds left and New Orleans grabbed the rebound on the miss.
Roberts made a 3-pointer with nine seconds left to pull the Hornets within 89-88.
Durant made 1 of 2 free throws with 8.1 seconds left. The Thunder scored 34 points in the fourth quarter, two fewer than they did in the first half.
"For whatever reason, we started the game off out of sync offensively," Brooks said. "Like I talk to the guys all the time and what we talk about every day, is that the defense needs to be there."
In the fourth quarter, Brooks said, "We got aggressive and I thought we passed the ball much better, but we were making shots. It was just a combination of a few things. Our defensive intensity picked up."
With help from 12 points by Ryan Anderson, New Orleans led most of the way in the first half and was up 44-36 at halftime. Oklahoma City, which entered the game second in the NBA in field-goal shooting at 49.1 percent, shot 30.6 percent from the field, including 0 of 3 from 3-point range.
Oklahoma City led briefly by one point on two occasions in the second quarter before a 13-3 run by the Hornets gave them a 36-26 lead.
Anderson finished with 14 points for the Hornets. Martin scored 17 for Oklahoma City while Russell Westbrook added 14.
NOTES: The Thunder's first-quarter (17) and first-half (36) point totals were season lows. ... The Hornets' only lead over the Thunder in the first two meetings of the season came in the second game, when they were up 2-0. New Orleans coach Monty Williams said before the game he's still not sure how long Eric Gordon, who has a sore left knee, will be out of the lineup.