The 34-year-old Jefferson made his fifth consecutive start in place of small forward Chandler Parsons, sidelined with a sprained left ankle, and hit five of six field goal attempts.
The Mavericks were led by Monta Ellis with 20 points. Rajon Rondo added 19 points, 15 in the first half.
The Pelicans, who entered on a five-game winning streak that equaled their longest in the last four years, were paced by Norris Cole with 19 points off the bench. Eric Gordon added 18 and Tyreke Evans 17.
After Dante Cunningham's jumper 20 seconds into the third quarter increased the Pelicans' lead to 60-55, New Orleans missed its next 12 shots as the Mavericks moved ahead 71-60 lead.
The Pelicans played without center Anthony Davis (shoulder), point guard Jrue Holiday (stress reaction lower right leg) and reserve forward Ryan Anderson (sprained right MCL).
Dallas outscored New Orleans 25-13 in the third period, limiting the Pelicans to 26.3 percent shooting from the floor.
The Mavericks also outscored the Pelicans 50-24 in the paint and tied a season low with seven turnovers.
Dallas played its third consecutive game without center Tyson Chandler (bruised left hip).
The Pelicans hit nine of 17 shots from 3-point range in the first half while grabbing a 58-55 lead. They got 28 points off the bench, led by Cole (13) and Alexis Ajinca (10).
Dirk Nowitzki, Dallas' second-leading scorer at 17.7 points per game, took only two shots in the half and had three points.
The Pelicans used a 10-2 run to build a 47-42 lead with 5:59 remaining in the half. Dallas responded with a 10-point run, including three field goals by Ellis, to move ahead 52-47 with 3:17 left before the break.
The victory kept the Mavericks a half-game behind the fifth-place Los Angeles Clippers in the Western Conference.
New Orleans, seeking its first playoff berth since 2011, dropped a game behind eighth-place Oklahoma City in the West.
Pelicans: Cole has scored in double figures in five of six games since being acquired from Miami. . Ajinca had 13 points and a game-high 12 rebounds.
Mavericks: Bernard James, on the ninth day of his second 10-day contract, made his second start at center. . Amare Stoudemire played his most minutes with the Mavericks (20) and equaled his scoring high with the team (14 points).
The Pelicans host Detroit on Wednesday.
The Mavericks begin a three-game road trip at Portland on Thursday.