The Hungarians took the lead from the penalty spot through Krisztian Kenesei, but then Jason Koumas and Robert Earnshaw struck to gave Wales victory.
Hungary started well and Sander Torghelle should have done better when he turned just six yards out, but he fired straight at Paul Jones in the Welsh goal.
Playmaker Zoltan Gera was the main thorn in the side for Wales early on as the away side struggled to pick up his deep runs.
Gera came close to breaking the deadlock but Jones parried his volley from the edge of the area wide of the goal.
Hungary then got the chance to make the breakthrough when Daniel Gabbidon was guilty of a clumsy challenge on Krisztian Lisztes and a penalty was given.
Kenesei stepped up confidently and converted with ease past Jones.
Wales, though, struck back almost immediately. They won a free kick on the edge of the Hungarian box and Koumas stepped up to curl a free kick round the wall and off the inside of Gabor Babos's right hand post.
Hungary continued to have the better of the play and Laszlo Bodnar struck a free kick just wide.
Gera maintained his dominance of the midfield in the second half but he was limited to creating mere half chances on the edge of the area.
Wales were limited hugely in the second period and their first real chance came with ten minutes remaining when Gareth Taylor almost beat Babos to a cross but he failed to get a touch on it.
With the game looking destined for a stalemate Wales then grabbed a shock lead.
Zsolt Low was under no pressure on the left when he attempted a clearance, but the ball flew off his foot backwards into the path of Earnshaw who raced into the area and turned back on to his right foot before lashing the ball home.
Hungary then pushed forward looking for a deserved leveller and the brilliant Gera almost found it with a superb acrobatic volley from the edge of the area, but substitute Danny Coyne pulled off a wonderful save low down to his right.
Hungarian boss Lothar Matthaus will be fuming with his side in his first home game since taking charge but Wales will be delighted to have again proved their credentials on the European stage.
Mark Hughes's side know they did not deserve victory, but winning without playing well is always the sign of a good team.
