Starting from pole position, Norris lost the lead to McLaren team-mate Oscar Piastri on the opening lap but fought his way back to the front to secure his first race victory of the season.
McLaren's hopes of a one-two finish were dashed with 15 laps remaining when Piastri retired with a gearbox problem while running second behind Norris.
Norris, the reigning world champion, won at the Hungaroring for the second successive year as he became the fifth different race winner in the last five grands prix.
Norris triumphed in the sprint race in Miami in May but had not taken the chequered flag at a grand prix since Sao Paulo last November.
Verstappen matched his best result of the season despite a difficult weekend for Red Bull.
Antonelli increased his lead at the top of the standings to 50 points over Lewis Hamilton after moving up from seventh on the starting grid, having incurred a three-place penalty on Saturday in qualifying.
Hamilton slid from fourth to fifth in the race after receiving a five-second penalty for speeding in the pit lane, dropping him behind Ferrari team-mate Charles Leclerc.
The season now heads into its summer break before resuming with the Dutch Grand Prix at Zandvoort on August 23.