Roland Sallai scored in either half for Hungary, who are top of Group A3
The Three Lions have now gone four games without a victory for the first time since 2014 and look worryingly out of form and confidence with a World Cup looming at the end of this year.
They could do nothing but capitulate to a humiliating and potentially damaging defeat that had the crowd booing and baying for Southgate's job at the final whistle.
Roland Sallai put the visitors in front with a well-taken finish at the back post, then doubled Hungary's lead with his second on the break 20 minutes from time.
There was more to come from a rampant Hungary, as Zsolt Nagy fired in from range and - after John Stones was sent off to compound a woeful evening for the hosts - Daniel Gazdag finished smartly to wrap up a second historic win over England in 10 days.
Jarrod Bowen had earlier missed a decent chance at the back post from Reece James' cross and Harry Kane flicked a header against the bar, but the hosts once again lacked the belief and inventiveness to open up their opposition.
Hungary - who top a group that also includes Germany and Italy - were well organised and clinical to earn only their second win over the Three Lions on English soil and first since a famous 6-3 success at Wembley in 1953.
The idea was the Three Lions would be buoyed by a packed and boisterous Molineux, after playing out a goalless draw against Italy in front of a couple of thousand schoolchildren on Saturday, but such is the brittle confidence in this England side at the moment that Hungary's opener knocked them off their stride and they never recovered.
Southgate made nine changes to the side that drew with Italy and England did start with some purpose when Reece James, from left-back, combined well with Kane before lofting a ball to the back post, where Bowen was unable to turn it in.
The West Ham forward should also have done better when England caught the visitors on the break after James had hooked off his own line to stop Hungary doubling their lead.
Substitute Phil Foden dragged an effort wide and Kane flicked a header against the crossbar, but the night belonged to Hungary as they showcased a clinical edge that England have been lacking throughout this international break.
What England have been throughout Southgate's tenure is solid at the back, not conceding more than once in 25 previous games before this one. But as Sallai pounced after Kalvin Phillips lost possession in midfield to double their lead, Nagy slammed in a third and Gazdag added a late fourth, that run was ruthlessly cut to pieces.
It brings a brutal end to a long campaign for these players, who will be grateful to take a break before pre-season begins with their clubs again in a few weeks.
But Southgate will be left to ponder this defeat knowing he has just two games left in September to arrest this slide before England head to the World Cup in Qatar, and also contend with the real possibility of relegation from the top tier of Nations League football.
Marco Rossi has created a resilient and hard-to-beat Hungary side, as England discovered in the opening Nations League game - one who took a point off Germany last time out and sat second in the group before this encounter in Wolverhampton.
But you have to go back to 1953 and the Magical Magyars' famous 6-3 victory at Wembley to find Hungary's only previous victory against the Three Lions on English soil, showing just what a monumental task the Italian is doing with this squad.
Having ground out a 1-0 win over England at the beginning of this international break, they showed that was no fluke with this resilient and clinical performance that delighted the 700 or so visiting fans at Molineux.
While Southgate's job will come into question after this performance, Rossi's stock is surely only on the rise having built a Hungary side who have proved they can mix it with the world's best.
-- Courtesy of BBC Sport