Captain Kevin De Bruyne scored twice and Youri Tielemans got the other as they dominated but were unable to register a more emphatic score.
A much tougher test lies ahead in Lyon on Monday against their neighbour, even if France’s Nations League campaign began with a surprise 3-1 defeat in Paris to Italy on Friday.
"We started well and scored straight away, but after the goal we lost some of our self-confidence", said coach Domenico Tedesco, who has been under pressure after Belgium made a disappointing round of 16 exit at the European Championship in July.
"Fortunately, we were sharper after the break, showed courage with vertical football and high pressure, in order to create quite a few chances again. That is a positive sign."
De Bruyne, who opened the scoring in the 21st minute and added a second-half penalty, had the same analysis after the match played behind closed doors in Hungary due to security fears.
"The first half was difficult as we had a hard time dealing with their defensive system. They played 5-4-1 and man-to-man on me. We didn't find the right combinations," he explained.
Created opportunities
"In the second half we were more patient and we did find the right players in the right places. That created more opportunities."
"It was a match with two faces," added Youri Tielemans, whose goal right after half-time put Belgium 2-1 ahead. "We had to focus more on ourselves before half-time. We conceded an unfortunate equaliser, but after the 2-1 we were able to play our own game.
"That I could score again myself? I have to keep that up now, right? I'm happy that I can be important again. Hopefully again on Monday. It's always a tough match against France," he said.
"When you play six group games, every game is important," De Bruyne added.
"We only have two days to rest and get ready. But the pressure will be on them now," he said of France, who eliminated Belgium at the Euros in Germany on July 1.
Asked whether his Manchester City manager Pep Guardiola would be happy if the 33-year-old played two full matches for Belgium inside four days, De Bruyne laughed in response.
"You'll have to ask him! Well, as long as I feel good, it's OK and it's up to the coach to decide. After France, I have six days before the next match with City."