The 19-year-old Italian built a big lead after starting from pole position in his Mercedes, but that evaporated after a late red flag to inspect a crumbling surface at the final corner following a crash that took out Ferrari's Charles Leclerc.
After a delay of around 40 minutes while repairs were carried out, the race resumed with a standing start but ice-cool Antonelli was unfazed as he became the youngest-ever winner of the iconic race.
Ferrari's Lewis Hamilton was runner-up for the second successive Grand Prix with Red Bull's Isack Hadjar third, although he was one of several drivers under investigation for a variety of infringements.
Hamilton, who equalled the late Ayrton Senna's eight Monaco podiums, moved above Antonelli's team mate George Russell into second place in the standings, 66 points behind Antonelli.
"We had incredible pace and it all came so naturally and that gave me the confidence to push."
A year after finishing last on his F1 debut at Monaco, Antonelli showed incredible poise to shrug off the red flag drama that meant he effectively had to win two races.
"I wasn't super keen on restarting, but once the notification came out, I just gathered my emotions and re-focused again. Once I got away and was P1 into the first corner, I could enjoy the last few laps."