Verstappen, who grabbed the lead on the first corner, finished 16.555sec ahead of Hamilton with Perez just over a second further back.
With six of the 21 rounds to race, Max Verstappen of Red Bull has retaken the lead in the drivers' championship by six points over reigning champion Lewis Hamilton of Mercedes.
Hamilton turned Verstappen's five-point championship lead into a two-point lead of his own as the Dutch driver finished second after a dramatic drive from last on the grid.
McLaren driver Lando Norris took pole after timing his final fast lap to perfection, in the dying seconds of the session after switching to slick tires as the racing line dried.
Hamilton clocked 1min 6.134sec in his Mercedes to beat Red Bull's Verstappen, the championship leader, with Valtteri Bottas in the second Mercedes third fastest.
Formula 1 2021: Ferrari’s Charles Leclerc on pole for Azerbaijan GP after crash-laden qualifying in Baku
Mercedes' world champion Lewis Hamilton will start alongside Leclerc, who is looking for quick redemption after taking pole in Monaco only to retire from the race when his car broke down on the warm-up lap.
Formula 1 2021: From Verstappen leading championship to Leclerc's elimination, talking points from Monaco GP
As expected, Qualifying in Monaco GP delivered more action than Race day. But even if Sunday didn’t deliver blockbuster action, it sure delivered a few very interesting narratives.
Formula 1 2021: Max Verstappen makes most of Charles Leclerc's Monaco GP misery to take championship lead
Carlos Sainz for Ferrari took second with Lando Norris of McLaren completing the podium. Mercedes' Lewis Hamilton had a low key weekend, qualifying in seventh and finishing in seventh.
Qualifying was red-flagged towards the end of Q3 after Leclerc's smash, depriving the likes of Hamilton and Verstappen a chance to topple the man from Monaco's time of 1min 10.346sec with a flying lap.
Formula 1 2021: Red Bull's Max Verstappen fastest on first day of pre-season testing, Mercedes struggle
Verstappen, long regarded as heir apparent to seven-time world champion Hamilton, clocked a best time of 1min 30.674sec in the Red Bull.
Ferrari mustered a mere 131 points compared to over 500 in 2019, and came in an embarrassing sixth in the constructors table.
The 55-year-old Mini driver, aided by co-pilot Edouard Boulanger, finished 14min 51sec ahead of Qatari Nasser al-Attiyah (Toyota), with Spain's Carlos Sainz rounding out the podium in another Mini.
A jubilant Brown said McLaren had "a great year" after Lando Norris and his Ferrari-bound team-mate Carlos Sainz finished fifth and sixth in the Abu Dhabi Grand Prix.
Launched in 1979 between Paris and the Senegalese capital Dakar the celebrated endurance challenge moved to the kingdom for the first time this year after a decade in South America, sparking angry reaction from human rights organisations.
Ferrari team chief Mattia Binotto spoke of how Vettel reacted: "Did Seb get in the way? No. He did not hang up the phone...He was never negative – instead he was pro-active and he was a very respectable person."
French driver Pierre Gasly's car caught fire on Friday while there was a crash between Red Bull's Max Verstappen and Lance Stroll's Racing Point car.
Formula 1 2020: Lewis Hamilton tops final practice at Russian Grand Prix ahead of Mercedes teammate Valtteri Bottas
Hamilton clocked a best lap of 1min 33.279sec to beat Bottas by seven-tenths with Carlos Sainz third for McLaren, eight-tenths off the pace.
Formula 1 2020: Pierre Gasly races to stunning victory at Italian GP as Lewis Hamilton handed penalty
Pierre Gasly finished 0.415 seconds ahead of McLaren driver Carlos Sainz and 3.358 ahead of Racing Point's Lance Stroll on a surreal-looking podium.
Formula 1 2020: Lewis Hamilton claims pole position in Italian GP qualifying, Valtteri Bottas takes second
It was Hamilton’s record-increasing 94th career pole position, his sixth in seven races and his seventh in Italy.
Formula 1 2020: Eight drivers summoned by stewards over Lewis Hamilton near-miss during Italian GP practice
As a result of the incident, when Hamilton changed direction at around 300 kph, he was summoned along with Nicholas Latifi, Romain Grosjean, Sergio Perez, Pierre Gasly, Lance Stroll, Alex Albon and Carlos Sainz to explain what happened.