Mexico’s Perez, who is only in his second race for Red Bull, lines up alongside the seven-time Mercedes world champion for what will be his first start in first place.
Verstappen, fastest in final practice on the Italian circuit and chasing a hat-trick, had to settle for third place with Ferrari’s Charles Leclerc, a solid fourth on a home track for the revived Italian side.
Hamilton did enough with his first flight lap of 14.411 seconds, but Perez came close at the end with just 0.035 slower effort.
“I certainly didn’t expect we owed two Red Bulls,” said Hamilton, who won the season opener in Bahrain last month after Verstappen left on pole.
“I think they were so quick this weekend, there were times when they were six tenths ahead.
“I got to the last corner and heard I got the pole and I was very grateful,” added the 36-year-old, who has now taken the poles on a record 30 different circuits.
Perez, who has over a decade of Formula 1 experience, has come to put more pressure on Mercedes than Verstappen’s recent teammates succeeded and duly delivered.
The Mexican still thought he could have done better.
“I got better, P2, but I should have been on pole and made a mistake on the last corner,” said Perez, a first winner with Racing Point (now Aston Martin) in Bahrain last year. .
It was the first time Verstappen had been overqualified by a team-mate in regular conditions since Australia’s Daniel Ricciardo was alongside Red Bull in 2018.
“You can’t be good every time, so we’ll see what went wrong,” said the Dutch driver. “It’s still P3, which is a good starting position.”
Pierre Gasly of AlphaTauri qualified fifth with Ricciardo sixth for McLaren and his teammate Lando Norris seventh.
Norris would have been in the front row if his fastest lap hadn’t been called out for going over the limits of the track.
Hamilton’s teammate Valtteri Bottas, on pole at Imola last November and fastest on Friday, qualified a disappointing eighth – leaving Hamilton exposed in Sunday’s race with the Red Bulls also on different tire strategies.
Hamilton will start on medium tires, with Perez on soft tires and Verstappen also on medium tires.
“Anything can happen, we’re on a different strategy than Lewis and Max,” Perez said. “This is going to be interesting, see what we can do.”
Spaniard Carlos Sainz, in his first race in Italy with Ferrari, failed to qualify for the final shootout and started 11th.
Both Williams riders reached the second phase for the first time since last July, with George Russell still looking disappointed in 12th place as he edged past former champions Sebastian Vettel and Fernando Alonso.
Quadruple champion Vettel will line up 13th for Aston Martin and Alonso, winner at Imola with Renault in 2005 on his way to the first of two titles, 15th for Alpine.
Japanese rookie Yuki Tsunoda was the big victim in the first session, losing control of the Alta Variant and smashing his AlphaTauri back into the tire wall.
“For me it was a huge mistake and I am very sorry for the team,” he said, with the session marked red as the badly damaged car was taken off the track.
Qualifications were brought forward by an hour as a token of respect to ensure there is no overlap with the Windsor funeral of Britain’s Prince Philip, who died last week at the age of 99 years.
The teams, most of which are based in England, kept a minute’s silence before qualifying.
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