The Europeans led through Gyorgy Komaromi’s third-minute strike at Goiania's Estadio Olimpico, before taking the lead again through Samuel Major eight minutes after Samson Tijani’s equaliser, to lead 2-1 at half-time.
A dramatic twist in the second-half then saw Manu Garba’s boys secure maximum points with goals from Usman Ibrahim and Oluwatimilehin Adeniyi.
It could prove a crucial victory for Nigeria, who lead Group B on goal difference, as a crunch meeting with Ecuador beckons on Tuesday.
For Olawale, dubbed 'Little Ronaldo' since his play-style resembles Juventus star Cristiano Ronaldo, the late rally is no coincidence as that reflects the inexorable spirit in the team.
"We are very happy that we won despite falling behind first,” Olawale told Goal.
"During the half-time break, coach Manu [Garba] told us to keep a positive mindset and we never gave up. That was what we did and got three goals in the second half.
"Hungary are a good team but they got tired towards the end of the game and it was more difficult for them to control our speed.
"Against Ecuador, we hope to be at our best again so that we can qualify for the knockout stage before taking on Australia.
"If we continue with our fighting spirit, I am confident that we stand a good chance of winning the title, but our focus for now is to take every game as they come."