Pontus Wernbloom's first international goals helped Sweden launch their bid to reach Euro 2012 with a comfortable home victory.
The 24-year-old was a regular scorer for IFK Gothenburg before departing to join Dutch outfit AZ 15 months ago, but he had not showcased that form in the Sweden shirt until tonight.
On his ninth appearance for his country, Wernbloom put Sweden in front after 51 minutes and then guaranteed three points in Solna by netting again after 73.
Sweden failed to qualify for the World Cup in South Africa, however they have reached each of the last three European Championships.
World Cup runners-up Holland are understandably the favourites to win Group E but Erik Hamren's side should have sufficient quality to finish as runners-up.
History suggests Hungary are unlikely to be serious threats, as they have not reached the finals since 1972.
Sweden had to wait for the goals to come tonight but were always on top. They threatened in the eighth minute when captain Zlatan Ibrahimovic crossed to Johan Elmander, whose header was easily saved by Gabor Kiraly.
Ibrahimovic, AC Milan's new striker, was again the creator of the next chance when his through-ball found Ola Toivonen who was also denied by Kiraly.
Zoltan Gera missed the target with his head at the other end, before Sweden left-back Emir Bajrami ran through on goal but slammed a shot wide of the right post.
Ibrahimovic should have scored twice before half-time but failed to make the most of two clear chances, however they were not expensive misses. Sebastian Larsson set up the opening goal, with Wernbloom heading his cross past Kiraly to end Hungary's resistance.
Vladimir Koman threatened an equaliser soon afterwards but failed with his shot, and Sweden doubled their lead when Wernbloom showed his strength in the air once again.
Kim Kallstrom swung over a corner and Wernbloom headed against the bar before meeting the ball on the rebound and this time finding the net.