Mercedes teammate Valtteri Bottas clocked the day's second quickest time of 1min 29.079secs, just 0.61secs behind Hamilton.
Verstappen, who grabbed the lead on the first corner, finished 16.555sec ahead of Hamilton with Perez just over a second further back.
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.
Bottas finished the 18-lap dash 2.325 seconds ahead of Verstappen but will start at the back of the grid on Sunday as he is going to take a new power unit and will receive a penalty for doing so.
Formula 1 2021: Ferrari's Charles Leclerc quickest in practice as Lewis Hamilton suffers engine problems
The seven-time world champion produced the fastest lap in a truncated morning session but lasted just three laps in the afternoon before his Mercedes ground to a halt with an engine problem on the Zandvoort circuit.
Formula 1 2021: Red Bull's Max Verstappen clocks fastest lap in Belgian Grand Prix practice before crashing
The Dutchman had set a best lap in one minute and 44.472 seconds to outpace Valtteri Bottas by 0.041 seconds and championship leader and seven-time champion Lewis Hamilton by 0.072 seconds before he ended the session after hitting the barriers at Malmedy.
Formula 1 2021: Mercedes star Lewis Hamilton quickest in final practice ahead of Hungarian GP qualifying
The Mercedes driver, who is aiming for the 100th GP win of his career this weekend, was just 0.88secs quicker than title rival Max Verstappen with Hamilton's teammate Valtteri Bottas in third, 0.229secs off the pace.
Roared on by a crowd of more than 140,000, Hamilton attempted to overtake Verstappen on Copse corner on the first lap instead sending the Red Bull careening off the track and into the barrier.
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: Sergio Perez wins chaotic Azerbaijan GP, Max Verstappen, Lewis Hamilton fail to finish
Sebastian Vettel for Aston Martin and Pierre Gasly for Alpha Tauri completed the unexpected podium.
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.
Mercedes didn't challenge for the top positions, with Lewis Hamilton seventh and Valtteri Bottas 10th.
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.
Formula 1 2021: Pole-sitter Charles Leclerc’s Monaco GP hopes dashed as Ferrari announce last-minute withdrawal
With Leclerc, who had damaged his car in a crash at the end of Saturday qualifying, out and his front-row spot vacant, Max Verstappen for Red Bull was left leading the grid for this fifth leg of the Formula One season.
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.
Leclerc held the top spot at his home track until his Ferrari grazed a barrier to break a suspension piece. He then hopped a curb and finally came to a stop crashed into another barrier to bring the qualifying session to an abrupt end.
Leclerc only managed a handful of laps in the morning after gearbox problems, but under crisp blue skies showed he can't be discounted in Sunday's fifth GP of the season.
Formula 1 2021: Mercedes' race-winning strategy, competitive Ferrari performance and other talking points from Spanish GP
Lewis Hamilton and Mercedes used a combination of race strategy and on-track overtaking to reclaim the lead at the 2021 Spanish Grand Prix
Formula 1 2021: Lewis Hamilton tops Spanish GP second practice while Max Verstappen finishes distant ninth
Hamilton, who leads Verstappen by eight points in the Formula One standings, set the best time in the second session with a lap of 1 minute, 18.170 seconds.