Portugal, second in Group One a point ahead of Sweden, will secure a playoff place if they beat Malta at home on Wednesday.
They opened the scoring after 18 minutes when Cristiano Ronaldo's cross was blocked by goalkeeper Gabor Babos only for Simao to pounce on the rebound with a first-time left foot shot.
"The keeper dropped the ball and I got there first. It was an important goal and we are happy because finally we depend only on ourselves," Simao said.
Buoyed by the goal, Portugal created three more chances almost immediately. Simao's low drive was booted away by Babos, who moments later tipped away a header from his own team mate Vilmos Vanczak. Bruno Alves headed just over from the corner.
RONALDO DEPARTS
However, their rhythm was broken when Ronaldo limped off in the 27th minute, clutching the sprained ankle that had threatened to keep him out of the match.
Hungary took heart from the winger's departure and almost equalised when Balazs Dzsudzsak's low drive flew just wide of Eduardo's goal. Just before the break Zoltan Gera's header hit the bar after Babos missed the ball coming out for a cross.
But Portugal then took control of the match again, with Pedro Mendes putting in a fine midfield performance to prevent the Hungarians posing any further danger in the second half. Mendes had any not played in the qualifiers so far, but Queiroz praised his contribution to the team.
"Mendes had an excellent game. I was counting on his experience," Queiroz said.
"When it became clear Tiago could not play, we needed to bring in a player like Mendes as we needed players with experience and quality to overcome a difficult Hungarian side."
The Portuguese forced Babos to make several good saves, but Liedson headed a deserved second goal from a chipped cross by Bruno Alves in the 74th minute.
Five minutes later Simao capped a fine performance by scoring again with a powerful volley from a Duda pass.
