The early warning signs were there for Netherlands, with Roland Sallai striking the post with a thumping effort in the 17th minute, and the breakthrough arrived just past the half-hour mark, with the same player on the scoresheet.
Netherlands would not have been too concerned when Zsolt Nagy picked up the ball, but he delivered a sensational cross into the penalty box, and Sallai was on hand to convert into the back of the net.
The visitors incredibly had 84% of the ball in the opening 45 minutes of action, but Hungary scored with their only attempt on target, and Netherlands were finding it difficult to carve out clear openings in the Nations League fixture.
Netherlands did have a chance to score from an indirect free kick late in the first half after a mix-up at the back involving goalkeeper Denes Dibusz and Dominik Szoboszlai, but the Hungarian stopper managed to keep out Cody Gakpo's effort.
Ronald Koeman's side were reduced to 10 men in the 79th minute when Van Dijk picked up a second booking in quick succession for a lunge on Kevin Csoboth, giving Holland a mountain to climb.
However, Netherlands managed to level the scores in the 83rd minute when Denzel Dumfries headed a brilliant free kick from Gakpo into the back of the net to earn his side a point.
The result has left Netherlands second in Group 3 of League A, boasting five points from their opening three matches, while Hungary sit in third spot, having collected two points from their first three matches.
HUNGARY VS. NETHERLANDS HIGHLIGHTS
32nd min: Hungary 1-0 Netherlands (Roland Sallai)
Hungary make the breakthrough in the 32nd minute of the contest through Sallai; Nagy delivers an excellent cross into the Netherlands box, and the number 20 is on hand at the far post to convert into the back of the net.
79th min: Virgil van Dijk red card
Netherlands are reduced to 10 men in the 79th minute of the contest, as Van Dijk picks up a second yellow card for a lunge on Csoboth, who was breaking into a dangerous position.
83nd min: Hungary 1-1 Netherlands (Denzel Dumfries)
Netherlands level the scores in the 83rd minute of the contest, as Dumfries heads a free kick from Gakpo into the back of the net. Huge moment for the 10-man visitors!
MAN OF THE MATCH - ZSOLT NAGY
Nagy was the star of the show on Friday night, with the left-sided wing-back putting in an excellent performance for Hungary, and it was his brilliant assist that allowed the hosts to make the breakthrough.
The 31-year-old had an excellent game all-round, though, winning four tackles, with his defensive work particularly crucial when Netherlands were threatening the Hungarian goal.
BEST STAT
HUNGARY VS. NETHERLANDS MATCH STATS
Possession: Hungary 26%-74% Netherlands
Shots: Hungry 6-16 Netherlands
Shots on target: Hungary 1-4 Netherlands
Corners: Hungary 2-5 Netherlands
Fouls: Hungary 19-8 Netherlands
WHAT NEXT?
Netherlands will be bidding to return to winning ways when they head to Germany on Monday night, but they will be without the services of Van Dijk following his red card on Friday night.
Hungary, meanwhile, will be bidding to build on what was a positive performance against Koeman's side when they take on Bosnia-Herzegovina on Monday evening.