In a game marred by fighting in the stands between Hungary fans and police, the visitors went ahead with a Roland Sallai penalty after 24 minutes, with England equalising in the 37th through John Stones after a Phil Foden free kick.
England were packed with attacking talent but were unable to impose themselves on a team they beat 4-0 in Budapest last month and created few further chances against the battling Hungarians.
The result leaves England top of the section on 20 points, with the Albania v Poland game still being played.
The Euro 2020 runners-up are still strong favourites to win the group via their remaining games against Albania and San Marino next month, while Hungary, in fourth place on 11 points, need a miracle to snatch second place and a playoff berth.