Gareth Southgate's team has secured four wins from four qualifying matches to open up a five-point lead over Poland, who face England in Warsaw after Sunday's meeting with Andorra at Wembley, at the top of Group A.
In a match that contained several points of tension in the crowd, including a loud hubris when England's players took the knee before kick-off, objects thrown and racist chants, they came through a modest first half for full control after the break and ran out of easy winners.
England captain Harry Kane missed a great opportunity to give them the lead shortly after the break, but it did not prove costly as Raheem Sterling was crowned with a smooth move involving Declan Rice, Jack Grealish, and Mason Mount to slip home with his 16th goal in his last 24 international appearances after 55 minutes.
Sterling then turned provider eight minutes later as his deflected cross sat perfectly for Kane to head home, Harry Maguire adding a third as his header from Luke Shaw's corner slipped through the grip of Hungary keeper Peter Gulacsi.
In one of the many incidents, Shaw bathed with plastic cups before taking the corner, as did England's celebrated players after Maguire scored. Sterling suffered a similar fate after putting England in the lead when he took off his shirt to display a message in honor of a close friend who died a few days ago.
England's night was rounded three minutes after the second serious error gave Them a fourth for Gulasie as he allowed Rice's shot under his body.
Sterling leads England merry
England's path to Qatar now seems smooth - a performance that has strengthened their position as consistent candidates to come through their easily qualified group.
Southgate's team maintained their nerve and discipline in Budapest's disturbing and frightening surroundings, leaving Hungary fans' behaviour much to be desired, to increase the heat and ruthlessly punish their opponents as soon as they advanced.
England's defence was untroubling and Southgate's only disappointment was that the margin of victory could have been more convincing, with Kane and Sterling missing clear chances to pile more misery on the lacklustre Hungarians.
Sterling was once again England's main character, as he was at the Euro, scoring the goal that broke the deadlock before setting up The Second For Keyen.
Southgate will be happy with the way England carved out their first goal, with Rice winning possession before a superb link between Grealish and Mount set up Sterling to finish a component. It was exactly what he wanted from these players.
England now faces Andorra at home on Sunday before travelling to Poland for what is likely to be the toughest road game to Qatar in Warsaw next Wednesday - but it is already difficult to know who can stop Southgate's team from returning to the World Cup next winter.