Hazard, who has finally burst into life at the tournament after a disappointing club season with Chelsea, set up one goal and scored another as Toby Alderweireld, Michy Batshuayi and Yannick Carrasco completed a comfortable victory overnight, Australian time.
“If he’s feeling good, he’s the best in the world,” Belgium goalkeeper Thibaut Courtois said of Hazard.
“The only thing we might have done better was kill the match off earlier.”
Belgium dominated the opening stages and took the lead after 10 minutes when Kevin De Bruyne swung an inviting cross into the box where centre back Alderweireld rose at the far post to power a header past keeper Gabor Kiraly.
Substitute Batshuayi tapped home Hazard’s low cross with 12 minutes remaining shortly after coming on before the Belgium skipper cut inside Hungary’s box and rifled home a superb low strike for the third, with Carrasco grabbing a late fourth.
Hungary, shorn of influential midfielder Lazlo Kleinheisler who was injured in the warm-up, ceded the initiative early as Belgium found space and set the tone for the match.
Meanwhile, world champions Germany eased into the quarter-finals of Euro 2016 with a comprehensive 3-0 victory over Slovakia in Lille.
Germany stamped their authority on the game from the start and could even afford a Mesut Oezil penalty miss as Jerome Boateng in the eighth minute and Mario Gomez in the 43rd put them two goals ahead before the break.
Julian Draxler hooked in the third in the 63rd minute to crown a man-of-the-match performance by the Wolfsburg midfielder.
The victory sets up an encounter with either Italy or title-holders Spain in Bordeaux on Saturday.
Italy and Spain meet tonight in Saint-Denis.
“Like a lot of teams we have also had problems in the tournament, but today it was overall a good performance,” Germany coach Joachim Loew said.
“It is also a good feeling when the team is good defensively, but now we are facing another calibre of opponent in the tournament.”
Slovakia midfielder Marek Hamsik said it had been a difficult match.
“We put in the perfect performance against the world champions,” he said.
“It’s a pity (to go out) but when we look at what we have done, we can be proud of ourselves and happy about what we achieved. We can build on this.”
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