The seven-time world champion put his Friday struggles behind him in a show of pace at a circuit where he has claimed a record eight victories, outpacing Red Bull's defending double world champion by 0.250 seconds.
After a tortuous day on Friday, Sergio Perez recovered to post the third-best time in the second Red Bull ahead of Nico Hulkenberg of Haas, McLaren's Lando Norris and George Russell in the second Mercedes.
Charles Leclerc was seventh ahead of his Ferrari team-mate Carlos Sainz, two-time champion Fernando Alonso of Aston Martin and Alfa Romeo’s Valtteri Bottas.
After Friday’s wet conditions, Saturday’s session offered a dry track and blue skies as Daniel Ricciardo led the way out of the pits in his Alpha Tauri.
The returning Australian was briefly fastest before the senior Red Bull team joined the fray, Perez going top only to be replaced by Verstappen in 1:18.748.
The opening two sessions were also affected by F1's latest rule change, this time with tyre-allocation, each driver being allocated 11 sets instead of the previous 13 and ordered to use certain compounds in each part of qualifying.
As a result, both Mercedes and Red Bull limited their Friday running. Hamilton used only one set of mediums and reported his car was "at its worst" while his team made clear they would welcome Nyck de Vries back in a reserve role after the Dutchman had been dumped abruptly by Red Bull.
After 25 minutes, the champion remained on top and Ricciardo was last, but the Mercedes were showing promise after overnight set-up changes. Hamilton was ninth and Russell 13th.
"Is everything ok with the rear?" asked Verstappen on team radio. "It's a bit weird."
His question reflected the strength of the changeable wind, notably at Turn Two.
Others continued to match the Dutchman's lap in vain until Alonso took command in 1:18.350 on soft tyres to beat his lap by one-tenth. Twenty years after his maiden F1 triumph at the Hungaroring, this was a reminder of the Spaniard’s raw pace.
With 15 minutes remaining, Norris, on new mediums, went top in 1:18.082 as the track evolved more rapidly in the closing minutes. Hamilton then showed his potential on softs with an outstanding lap in 1:17.811 to move clear by two-tenths, enough to keep Verstappen at bay on his first soft tyre run.
"No grip!" declared a frustrated Verstappen, demonstrating how critical tyres will be later in qualifying and for Sunday’s race – and how adroitly Mercedes had once again managed to turn apparent difficulties on Friday into an upsurge of pace on Saturday.
