"I didn`t see it coming, but after the first stint it seemed like we were really good on tyres," said Verstappen as he celebrated a ninth career win that lifted him to 77 points with Hamilton on 107.
Mercedes had won the delayed season`s four previous races and taken every pole, but Verstappen was alone among the top 10 on the grid to start on the hard tyres.
The British racer then took to Twitter and expressed that the last lap almost had him.
Hamilton raced at an average speed of 237.6 km/h and gained 25 points.
The 27-year old suffered the injury when he crashed during the Spanish Grand Prix in Jerez on July 19.
The Repsol Honda rider travelled to Barcelona on Monday and was treated at the Hospital Universitari Dexeus.
Marc will remain in the hospital for up to 48 hours.
Hungary is also a favourite for Hamilton, who has won there seven times and can equal Schumacher`s feat of winning the same Grand Prix eight times.
"Every time I`m reminded of the records that Michael had, it`s just still mind-blowing to me," Hamilton said.
The race, again without spectators due to the COVID-19 pandemic, will be a tough one for all involved since strict rules in Hungary mean teams -- already in a bubble -- cannot leave their hotels other than to go to the circuit or airport.
"Renault is my family, my fondest memories in Formula One with my two World Championship titles, but I’m now looking ahead," he said in a team statement.
The race, on a sunny afternoon at the scenic Red Bull Ring, was held in front of empty grandstands and no fans for the first time due to the COVID-19 pandemic.
Four-times champion Sebastian Vettel failed to reach the top 10 shootouts, starting 11th, while Charles Leclerc qualified seventh after taking pole last year.
Germany`s Sebastian Vettel Sebastian Vettel’s future in Formula 1 beyond 2020 has been thrown into doubt after it was announced on Tuesday that he will leave Ferrari at the end of the season.
Formula One is currently working on a revised calendar for the 2020 season after the pandemic forced a series of postponements and cancellations of races.
The league which is scheduled to be held between November 30 and December 1 in New Delhi at the Buddh International Circuit and December 7 and 8 at the Madras Motor Race Track in Chennai will comprise of two cars and two drivers in each car for each team.