Russell got away cleanly at lights out and never looked challenged over the 24-lap sprint race, outpacing Ferrari's Charles Leclerc, who finished second, by 1.36 seconds.
Leclerc's battle with current world champion Lando Norris was the highlight of the race, the Ferrari overhauling the McLaren in a thrilling overtake on the straight in the 18th lap.
"Obviously a great start to the weekend. If it was one more lap, it would have been a very potentially different end to the race, so glad the rain came when it did," said Russell, after the heavens opened at the chequered flag.
Norris, who complained of problems with the rear of his McLaren, came in third, just managing to hold off teenage sensation Antonelli.
"I just don't have the pace. There's nothing we can do," a downcast Norris told reporters.
Antonelli started fifth on the grid after running into the gravel during qualifying and damaging the floor of his Mercedes.
He did manage to jump McLaren's Oscar Piastri at the start to gain a place, coming in fourth with the Australian finishing fifth.
Home favourite Max Verstappen, on a high after extending his Red Bull contract until 2030, failed to improve on his grid position, ending up sixth.
He had an enjoyable tussle with seven-time world champion Lewis Hamilton, the battle between two legends of the sport exciting the Zandvoort crowd.
'Real fight'
Later Saturday, the drivers will wrestle for pole position for Sunday's Grand Prix, which promises to be one of the most open races of the season.
Very little separates the top three teams -- Mercedes, Ferrari, and McLaren - and Red Bull's Verstappen can never be ruled out in his home Grand Prix.
After the sprint race, Antonelli holds a 53-point lead over his closest rival Hamilton but with every sign the gap could narrow towards the end of the season.
Antonelli and Mercedes dominated the first half of the season, with the prodigy picking up wins in six of the 11 races, including five consecutive chequered flags.
But the chasing pack have brought successful upgrades to their cars, with Mercedes admitting they are "out of sync" in terms of improvements to their own package.
"It's so close, you know yesterday there was a tenth (of a second) between the top four drivers," said Russell.
"There's probably six drivers all in the fight for pole... We have a real fight on our hands these days," added Russell, fresh from getting engaged during the summer break.
"I think that's quite fun and that's how Formula One should be - it shouldn't just be two teammates going for race wins week in week out. Everybody should be in with a shot."
Sunday's Grand Prix will be the last edition for the Dutch since the Zandvoort circuit was reintroduced to the calendar in 2021.
Despite attracting big crowds eager to see Verstappen, promoters have pulled the plug, saying the financial risks were too great.
