D'Antoni was hired by the Lakers last week but had only been able to take the team through practices due to knee surgery.
His offense-oriented style helped the Lakers to their highest scores of the season in their last two games but on Tuesday it was their defense that secured the win.
Kobe Bryant scored the Lakers' final eight points, finishing with 25, and Los Angeles (6-5) held the visiting Nets scoreless during a near three-minute stretch late in the fourth quarter to pull out their third straight victory.
Brooklyn (6-3) had a six-point lead midway through the fourth, but went cold in the closing moments and saw their five-game winning streak snapped.
"Really happy to get a win, obviously," D'Antoni said. "We didn't play well overall but to outplay a team that won five in a row, that means something. (Physically), I feel good. Adrenaline is a good thing."
Deron Williams misfired on a potential game-tying three-pointer with four seconds left. He finished with 22 points and 10 assists while team-mate Brook Lopez added 23 in the loss.
"We were right there and we battled the whole game," Williams said. "We just didn't make enough plays down the stretch."
The Nets have been on a tear this season since moving from New Jersey to Brooklyn, and a win would have matched their best start to a campaign since the 2002-03 season.
Under coach Avery Johnson, Brooklyn had been thriving on defense and entered the game allowing just 92.5 points per game.
The Lakers looked determined to shatter that mark early, scoring the game's first 10 points amid the excitement of D'Antoni's arrival.
But the Nets recovered to grab a 57-56 lead at half-time before defenses got the upper hand in the second half.
Brooklyn went ahead 86-84 with 3:23 to go but could not score again until pulling within one with 36 seconds remaining.
Bryant sealed the game at the free throw line where he closed things out with six in a row.
Dwight Howard struggled at the line, making just seven of 19, a blemish on an otherwise strong night that included 23 points, 15 rebounds and four blocks.
"The free throws will come, I'm still going to be aggressive," said Howard, who was intentionally fouled and put at the free throw line by Brooklyn several times late on.
But the spotlight was on D'Antoni, who received a standing ovation before the game then sat in a special elevated seat that the Lakers used to reserve for former coach Phil Jackson.
"I hope that's not (Jackson's) chair. I hope it's my chair," D'Antoni joked. "I'm just keeping it warm."
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