Piastri, who'd started in seventh on the grid, made a neatly timed thrust at the end of the penultimate lap to pass Ferrari's Charles Leclerc and seal third place behind his teammate, runner-up Lando Norris.
But there was frustration from world champion Norris that his McLaren team hadn't managed to seal victory at the Miami International Autodrome after a race full of drama and incident, with the threat of rain hanging over proceedings, was completed without any weather interruption.
Ultimately, though, it was the 19-year-old championship leader Antonelli's day again as he overcame a disappointing start to regain control of the race and became the first driver ever to convert his first three poles into victories -- all in the space of just seven magnificent weeks.
The youngster increased his advantage in the title race to 20 points after four rounds. "It is just the beginning, the road is still long, but we're working super hard," Antonelli beamed.
It was another level-headed display, and a demonstration of his prodigious talent too, that despite losing the lead to Leclerc on the first lap, he quickly regained it and then, after Norris had assumed control, he took over for good with a brilliant outlap after Mercedes had stolen the key advantage by pitting ahead of McLaren.
After winning the Chinese and Japanese Grand Prix back-to-back, Antonelli has now become the third driver ever to earn his first three F1 wins in consecutive races, joining Damon Hill and Mika Hakkinen.
But Norris, who'd won Saturday's sprint, felt McLaren had been outmanoeuvred, asking over the radio: "How did we not win this? We should have won, guys."
Later he added: "I'm gutted to miss out on the win. It was a mixed bag, really. We just got undercut (by Mercedes), we should have boxed first."
Piastri wasn't complaining after his previous evening's qualifying struggle. He made a good start to initially move up to third from seventh, but re-emerged after his mid-race pitstop back in seventh before really finding some pace in the latter stages.
"The pace seemed more encouraging again today," he reported. "I had to make a few overtakes, obviously, and it was a pretty late charge late in the race, but it just very, very tricky around here, especially in these conditions.
"But clearly we're a step closer in performance once again. So that's nice to see."
Piastri's final push came on the 56th of the 57 laps, as he roared past Leclerc, who was struggling so much by then that he subsequently lost control with a last-lap spin and brushed the wall, enabling fourth-placed George Russell and fifth-placed Max Verstappen to pass him.
So there was drama right to the end, just as there had been at the very start when Leclerc had actually benefited from Verstappen's Red Bull spinning 360 degrees in mid-track as he strained too hard to move from second on the grid.
Verstappen, who worked wonders to stay in control, dropped initially to 10th so had to be satisfied with his ultimate fifth spot.
The race had been moved up by three hours to avoid thunderstorms, making for what Piastri called a "very tricky" day as teams prepared for and tried to anticipate the bad weather that never came.
The safety car was deployed on lap six after two accidents, when Red Bull's Isack Hadjar skidded into the wall and then Alpine's Pierre Gasly went cartwheeling off after contact with the Liam Lawson's Racing Bulls.
