Germany's makeshift midfield, with Bayern Munich's Bastian Schweinsteiger being granted a few days of extra rest, looked strong with the 23-year-old Khedira in top form.
Ballack was ruled out of the June 11-July 11 tournament in South Africa last week with an ankle injury.
In other matches, Spain left it late to secure a 3-2 victory over Saudi Arabia and the United States came from behind to edge out Turkey 2-1.
At Budapest, Khedira, who now looks set to partner Schweinsteiger in central midfield at the World Cup, was lively in his fourth international appearance, repeatedly slicing open the Hungarian defence at will with quick, accurate passing in the first half. Lukas Podolski fired Germany into an early lead with a powerful penalty and Mario Gomez added another in the 69th minute from close range before substitute Cacau netted his third goal in his last two matches with a fine solo effort in the 72nd minute.
At Innsburck, Fernando Llorente headed a last-minute winner for Spain in a 3-2 victory over Saudi Arabia on Saturday as the European champions made a sluggish start to their preparations.
Spain should have felt at home in the Tivoli Neu stadium as it was where they beat Russia 4-1 to kick off their successful Euro 2008 campaign, but they fell behind to an Osama Hawsawi header in the 17th minute.
David Villa and Xabi Alonso scored either side of the break but a deflected shot from Mohammad Al-Sahlawi in the 75th minute put the Saudis level, before Llorente headed in at the end. "This kind of thing happens sometimes but we have to be positive; we started a little lazily because we have had 15 days without playing and we found it hard to get into it," Spain coach Vicente del Bosque told Spanish state television.
"I'm not happy with everything. We are a little behind because we have these 15 days without playing but we have to remain optimistic."
Spain captain and goalkeeper Iker Casillas made his 103rd appearance to become the country's second most capped player.
Andres Iniesta, who looked lively on the left flank after recently recovering from a thigh injury, set up Spain's equaliser after defender Hawsawi had put the Saudis ahead.
The Barcelona midfielder cut back inside his marker and floated a cross for Villa to nod in unmarked from close range.
By then, Spain were in charge and when a counter-attack broke down early in the second half, Alonso picked up the loose ball and drilled a low shot into the corner from outside the area.
Del Bosque gave Barca forward Pedro his first cap soon afterwards as he started making changes but the Saudis surprised Spain again, with Al-Sahlawi firing in a deflected shot. Athletic Bilbao midfielder Javi Martinez won his first cap as a substitute just after the equaliser but it was his club-mate Llorente who spared Spain's blushes by heading in from a corner in the final minute.
In Philadelphia, Jozy Altidore and Clint Dempsey scored second-half goals for the United States, who came from behind to beat Turkey 2-1. The US struggled in the first half and Turkey, coached by Dutchman Guus Hiddink, had two good chances before taking the lead in the 27th minute when Arda Turan finished off a smart counter-attack. Donovan had a hand in the winner as well, playing the ball through to Dempsey who held off a challenge from Sabri Sariogulu.
