But to everyone's surprise, hard tyres were put on the 24-year-old Monegasque driver's car.
Alpine drivers Esteban Ocon and Fernando Alonso had been struggling to find any pace on the hard tyres for several laps, so Ferrari's strategy baffled many.
"Wow, that is brave considering how the hards are going for everyone else," Sky Sports reporter Ted Kravitz said.
And less than two laps later, Leclerc was overtaken by Red Bull rival and championship leader Verstappen.
"F***, the tyres are ****," Leclerc said on the team radio.
"Oh my God. So bad.
"That's why I said I wanted to stay on the medium as long as possible."
Leclerc was given a reprieve, however, with Verstappen spinning moments later and giving back the position, but it didn't take long for the Dutchman to overtake him once again.
Verstappen and seven-time world champion Lewis Hamilton were overheard laughing about Ferrari's strategy in the cooldown room.
"(Leclerc) was struggling on the hard tyres," Verstappen admitted after the win.
The Ferrari driver's pace in the hard tyres was so bad that he was forced to pit again and change into soft tyres, emerging from the pit lane in sixth.
Sky Sports commentator David Croft said: "In a season where Ferrari have already cost themselves dearly in terms of reliability, in terms of accidents in terms of strategy... you can add the Hungarian Grand Prix to that list."
Mercedes drivers Hamilton and George Russell finished second and third respectively, while Australia's Daniel Ricciardo placed 15th.
There were few scary moments throughout the race - AlphaTauri's Yuki Tsunoda went for a spin on Lap 35, while Alfa Romeo's Valtteri Bottas retired on the penultimate lap, forcing a late virtual safety car.
Rain also started falling on the track with a couple of minutes remaining, meaning Verstappen had to tip-toe his way towards the finish line.
But the reigning world champion kept his composure and got the job done, winning his eighth race of the season.
"I was at first hoping that I could get close to a podium, but very tricky conditions out there but we had a really good strategy," Verstappen said.
"We were really reactive and always pitting at the right time, I thought we had some good out laps, and at the end – even with the 360 – we won the race.
"It was a crazy race and I'm of course very happy that we won it."
Hungarian Grand Prix Results
1) Max Verstappen, Red Bull
2) Lewis Hamilton, Mercedes
3) George Russell, Mercedes
4) Carlos Sainz, Ferrari
5) Sergio Perez, Red Bull
6) Charles Leclerc, Ferrari
7) Lando Norris, McLaren
8) Fernando Alonso, Alpine
9) Esteban Ocon, Alpine
10) Sebastian Vettel, Aston Martin