It was the fourth straight win for the Bucks, who finished their first half of the season in third place in the Eastern Conference.
Zion Williamson scored 34 points and Brandon Ingram added 23 for the Pelicans, who had won two straight.
The Bucks won their previous three games by an average of 17.7 points. In those games, Antetokounmpo averaged 34.7 points, 15 rebounds, 6.7 assists, 1.7 blocks and 1.3 steals.
But Thursday’s game was tight. There were 15 ties and 23 lead changes.
“Last two years, we were beating teams by 15, by 20, by 30, but at the end of the day, that did not make us better,” Antetokounmpo said. “I think when you’re getting a game every single night, it’s a dogfight, you fight to win, it helps you. It helps you in the long run, we build good habits and hopefully it can help us in the playoffs.”
New Orleans took a 125-124 lead with 2:01 to play in the fourth quarter on a layup by Williamson. But after Antetokounmpo hit a jumper and then took a rebound the length of the court for a dunk, Milwaukee led 128-125 when New Orleans called timeout with 1:10 left.
Ingram and former Buck Eric Bledsoe missed 3-pointers and Ingram committed a charge before time ran out.
“I thought we got some really good looks down the stretch, passed up two good looks, I thought, but had some other good looks that could have gone down,” New Orleans coach Stan Van Gundy said. “I don’t think down the stretch that we were having trouble getting shots.
“We just didn’t make them.”
Milwaukee’s Donte DiVincenzo had a career-high 24 points.
Antetokounmpo and Williamson showed their knack for getting to the hoop, with their first-quarter performances as evidence. Williamson’s 11 points included a drive past Antetokounmpo to score with a right-hand layup, two dunks and a putback of his own missed dunk. Antetokounmpo’s 13 points included a turnaround hook and three layups.
It was the third matchup between the two superstars, with Antetokounmpo outscoring and outrebounding Williamson in both previous matchups.
Antetokounmpo is the first Bucks player with three straight 35-point games since Kareem Abdul-Jabbar in 1973, according to ESPN Stats & Info.
The teams entered Thursday among the top five in the league in field-goal percentage — with the Bucks ranked second at 48.8%; the Pelicans fifth at 48.3%. But they shot even better than their season averages, with Milwaukee shooting 54.2% and New Orleans 50% from the floor.
The Bucks have generally dominated their opponents in rebounding, entering with a league-leading average of 48.5 per game. But they were outrebounded by the Pelicans 47-42. New Orleans’ Steven Adams had 13 rebounds.
The Bucks prevailed without guard Jrue Holiday for the 10th consecutive game (health/safety protocol). Holiday, who was acquired from New Orleans in a four-team trade in November that sent Bledsoe to New Orleans, is averaging 16.4 points and a league-leading 1.9 steals per game.
Pelicans: “I haven’t noticed it, I’ve got to be honest, I just haven’t,” Van Gundy said about fans being back in NBA arenas. “I don’t know that I ever do, unless you’re in a place that’s absolutely packed and going crazy.”
Bucks: G Bryn Forbes entered shooting 46.9% from 3-point range and 48.1% from the field, both career highs.
Pelicans: At San Antonio on Saturday. The Pelicans beat the Spurs 98-95 in the teams’ first matchup, in New Orleans on Dec. 27, despite shooting 38.3% and 20.8% from 3.
Bucks: Host the Clippers, who are 11-4 on the road, on Sunday. The Bucks last played the Clippers on Dec. 6, 2019, winning 119-91 in Milwaukee.