Behind the scoring of Thomas, the Kings took the lead late in the third quarter and never trailed in the fourth while snapping a three-game losing streak.
Rudy Gay added 14 points and Reggie Evans had 10 points and 13 rebounds for Sacramento, which outrebounded the Pelicans 47-30.
Tyreke Evans scored 14 of his 27 points in the fourth quarter and added 10 rebounds and eight assists for the Pelicans, who have dropped eight straight and 10 of 11. Brian Roberts scored 15 points and Eric Gordon fouled out in the fourth quarter with 10.
New Orleans All-Star forward Anthony Davis shot 4 of 14 and had 13 points. He missed his first 10 shots before making his first basket, a step-back 10-footer over Cousins, at the 9:10 mark in the third quarter.
Davis, who has been bothered by a sore left shoulder, was in foul trouble in Saturday's 32-point loss to the Clippers. He had one of his least productive games of the season, shooting 1 of 6 and scoring eight points.
It was the second game back in Sacramento for Evans, who played his first four seasons with the Kings before being traded last summer. He had 25 points, 12 assists and six rebounds in a Dec. 23 victory.
After the Pelicans cut the lead to five points, the Kings made three free throws and Gay hit a jumper midway through the fourth quarter for an 83-73 lead.
After a quiet first half, Thomas got going in the third quarter, scoring 11 points. The Kings closed the period with a 20-6 run and led 68-59.
Gordon hit a pair of 3s and Evans had another, putting the Pelicans ahead 52-46 midway through the third.
NOTES: Cousins made all nine free throws and scored 17 first-half points, helping the Kings to a 40-38 lead. ... Pelicans starting forward Ryan Anderson, who grew up in the Sacramento region, will likely miss the remainder of the season with a herniated disk. ... New Orleans missed all seven of its 3-point attempts in the opening half, while the Kings were 0 for 2.