Bam Adebayo scored 30 points and Tyler Herro added 27 for Eastern Conference leaders Miami, who were without starters Jimmy Butler, Kyle Lowry and P.J. Tucker.
Without their stars, the Heat trailed by as many as 16 points in the second quarter, but they closed the first half on a 19-10 scoring run and were down by just seven at halftime.
"This is a game we should win," said Jacque Vaughn, who stood in as Nets coach with Steve Nash in Covid protocols. "We told our guys that after the game. We should feel disappointed."
Durant, who had missed 21 games with a sprained knee ligament, showed no sign of rust as he scored 17 of his 31 points in the first half.
But Miami opened the third quarter on a 21-7 scoring run to take control, leading by as many as 12 points in the fourth period.
Brooklyn cut the deficit to two points with 2:23 remaining, but could get no closer.
The Nets had gone just 5-16 without Durant, sinking in the Eastern Conference standings.
Prior to the contest Durant said he felt "energized" but cautioned that he couldn't reverse the Nets' fortunes on his own.
Kyrie Irving was again sidelined at home because of New York's coronavirus vaccine mandate, and Durant was back in action for the first time since James Harden was traded to Philadelphia in February.
Nevertheless Durant and the Nets got off to a strong start, connecting on 57.4 percent of their shots in the first half, when they made nine three-pointers.
The Heat stepped it up defensively in the second half, limiting Brooklyn to 53 points on 33.3 percent shooting.
Durant acknowledged before the contest that with five weeks left in the regular season the Nets have a lot of work to do.
"We are cutting it close," he said. "But that's the situation we are in. That's the circumstances we are in. We have to go out there and figure it out."
Tatum out-duels Morant
In Boston, Jayson Tatum celebrated his 24th birthday with 37 points as the Celtics dominated Ja Morant and the Memphis Grizzlies 120-107.
Tatum added six rebounds and five assists for the Celtics, who notched their 13th win in 15 games.
Al Horford made four three-pointers on the way to 21 points with 15 rebounds for the Celtics. Marcus Smart had 18 points and 12 assists.
Memphis' explosive star Morant led all scorers with 38 points -- 30 of those coming in the second half after he struggled from the field before the break.
Morant's slow start and 11 first-half Memphis turnovers proved too much to overcome, especially with Tatum coming up with 27 of his points in the second half.
In Atlanta, the Hawks turned the tables on Chicago, denying the Bulls a four-game season sweep with a 130-124 victory.
Trae Young scored 39 points and Bogdan Bogdanovic drilled a three-pointer to put Atlanta up for good with 1:41 remaining.
In Los Angeles, the Clippers completed a four-game season sweep of the crosstown rival Lakers with an emphatic 132-111 victory.
Reggie Jackson scored 36 points for the Clippers, who out-scored the Lakers 40-18 in the third quarter to take control.
LeBron James scored 26 points for the reeling Lakers, who lost their fourth straight game.
In Dallas, Luka Doncic scored 41 points to lead the Mavericks to a 122-113 victory over Golden State -- their second win over the Warriors in five days.
The Mavericks never trailed on the way to a third straight win. The Warriors, meanwhile, dropped their third in a row for the first time this season and fell 7.5 games behind the league-leading Phoenix Suns in the Western Conference.