The 19-year-old Italian became the first F1 driver to claim his first three wins in a row from his first three pole positions, after triumphs in China and Japan had hoisted him to the top of the title race.
Driving with determination and elan, Antonelli struggled for ascendancy in the first part of the race before enjoying an "undercut" pit stop to win his duel with Norris in the closing stages.
In the first race following a five-week hiatus due to the conflict in the Middle East, Antonelli came home first, 3.264 seconds clear of Norris and his McLaren team-mate Oscar Piastri, who finished third 23.828 seconds adrift.
Antonelli's Mercedes team-mate George Russell, who began the season as championship favourite and won the opening race in Melbourne, finished fourth ahead of Red Bull's fiery and rejuvenated four-time champion Max Verstappen and Ferrari's Charles Leclerc, who spun on the penultimate lap.
Seven-time champion Lewis Hamilton came home seventh in the second Ferrari ahead of Franco Colapinto of Alpine and the two Williams drivers, Carlos Sainz and Alex Albon.
Mercedes had dominated the opening three Grands Prix and arrived in Miami as the only top team without an upgrades package. But despite losing to Norris in Saturday's sprint race showed they remain on top.
"What a race, man, woo!" exclaimed Antonelli on team radio after winning, "Oh my god!"
He later said: "The team did a great strategy and we had a massive undercut -- and I was able to bring it home. It was a tough race.
"I was a bit lucky when I locked up at the start behind Charles and then I did a mistake with energy management."
Norris described the result as "a mixed bag."
"We just got undercut. We should have boxed first, but Kimi did a good job and hats off to him and Mercedes," he said.
"A good race. He didn't make any mistakes and I'm gutted not to win, but I didn't have the pace."
The weather was significantly cooler than for Saturday's sprint, but without the forecast rain that had brought forward the start by three hours.
Antonelli made a clean start from his third consecutive pole, but was passed on the inside by Leclerc as Verstappen hit a curb and spun, creating chaos.
Leclerc resisted Antonelli with Norris third until lap five when the teenager passed him, only for Leclerc to regain the lead.
"Be patient, Lando, stay with them and let them yo-yo," said Will Jospeh, Norris's race engineer, before the luckless Isack Hadjar -- who had started from the pit lane -- crashed on lap six.
Almost immediately, Pierre Gasly also lost control, half-rolled and hit the wall after a collision with Liam Lawson, and a safety car was deployed.
Verstappen, who had fallen back, clashed with Lawson and Sainz, before pitting on lap nine for hards, returning in 16th. Lawson retired his damaged car, joining Nico Hulkenberg, Gasly and Hadjar in the pits.
Racing resumed on lap 12 with Leclerc resisting Norris until the champion powered by to become the third different leader as light rain arrived.
Driving with fury, Verstappen, who had crossed a pit lane exit line and faced a post-race investigation, climbed back to sixth by lap 21 when Russell pitted for hards.
Norris then led Antonelli by 3.2 seconds in the duel to define the race.
Leclerc pitted for hards and returned 10th, behind Russell.
"Why did we stop then?" asked a frustrated Leclerc. "When is the rain? Next time you make a decision, please speak to me..."
Antonelli then pitted, together with Norris and Hamilton, the champion losing the initiative to the young Italian as Piastri enjoyed a brief spell as leader before pitting.
This left the precocious Silver Arrows boy in front, with his team calming his nerves as McLaren's defending champion stalked him.
The pair were separated by less than a second after 40 laps.
After the frantic yo-yo passing of the early stages, the field stretched out when Leclerc passed Verstappen, on his long-worn tyres, before his late spin gifted Piastri third place.