The Spaniard, whose talks with various teams have been cited as stalling the Formula 1 driver market for next season, clocked a best lap of one minute and 18.713 seconds to beat the three-time world champion by 0.276 seconds.
Sainz, one of six different race winners this year, is set to leave Ferrari and be replaced by seven-time champion Lewis Hamilton of Mercedes next season.
His Ferrari team-mate Charles Leclerc was third fastest ahead of Mercedes' George Russell, Sauber's Zhou Guanyu and McLaren's Lando Norris and Oscar Piastri.
Yuki Tsunoda, harbouring ambitions to be promoted to Red Bull if the senior team parts company with the struggling Sergio Perez, was eighth for RB, ahead of Aston Martin's Lance Stroll and Hamilton, who was 10th for Mercedes ahead of Perez.
The top 10 were separated by little more than half a second, indicating a close contest lies ahead in both Saturday's qualifying and Sunday's race.
In searing heat, the session began with Russell showing the early pace on the tight and demanding Hungaroring.
Verstappen, in his updated Red Bull, swept to the top in 1:20.715 ahead of Norris, wearing a helmet designed specially to apologise for his part in breaking the trophy handed to Verstappen after winning last year's race.
Russell bounced back in 1:20.083, but Verstappen responded in 1:19.831 as the times began tumbling, Alexander Albon taking Williams to the top briefly before another hot lap from Russell lifted him clear again.
Russell's lap was followed by Hamilton slotting into second place behind him before Norris separated them with 25 minutes remaining.
Hamilton was only 0.150 seconds adrift, but it was not enough to keep a top-three spot in a closely contested session before Leclerc regained the initiative in 1:19.011.
If that lap proved the updated Ferrari was working better than it had at Silverstone, Sainz endorsed the impression with a lap in 1:18.713, taking him three-tenths clear of his team-mate.
After a spell in the pits to evaluate progress, Verstappen rejoined the fray and split the Ferraris, rising from 15th.
It seemed the updates worked, but it was too early to suggest Red Bull were poised to regain their luxurious advantage over their rivals.