McLaren's Oscar Piastri joined the Formula One championship leader provisionally on the front row, with the Australian summoned to stewards for possibly impeding Haas's Kevin Magnussen in the first phase.
"Incredibly happy to be on pole here. I didn't expect that," said Verstappen, who came close to the gravel on his final lap without paying a price.
Senna's run was set in 1988-89 with McLaren and Verstappen, like the late Brazilian a triple world champion, started his sequence in Abu Dhabi at the end of last season and has dominated qualifying in 2024.
Verstappen's 39th career pole came as Formula One marks 30 years since Senna, who had 65 poles, died in a crash at the Italian circuit on May 1, 1994.
"It's a great start to the year and very special," said the Dutch driver after also matching Alain Prost's record 1993 seven successive poles at the start of a season.
"It's 30 years since he (Senna) passed away, so very pleased to get pole and in a way it's a nice memory to him. He was an incredible F1 driver, especially in qualifying," added Verstappen.
The champion's fastest lap of one minute 14.746 seconds was 0.074 quicker than Piastri's best and came after he had struggled through all three free practice sessions.
Ferrari had been on top on Friday and Piastri, who was 0.017 faster than third-placed Lando Norris in qualifying, had led a McLaren one-two earlier on Saturday.
"It was pretty good, a little bit of a scruffy last corner but here it’s so, so difficult to do a perfect lap," said the Australian.
"I’ve been really comfortable with the car from the moment we put it on track yesterday. So, so close to pole, but very happy. It’s been a little while since I’ve been back up here."
Norris, a first time winner at the previous race in Miami, pipped Ferrari's Charles Leclerc at the Italian team's home circuit.
"We are getting closer. To be ahead of Ferrari is also a nice result for us," said Norris. "It's going to be close, it's going to be a good race tomorrow."
Perez starts 11th
Ferrari's Carlos Sainz qualified fifth, with Mercedes' George Russell sixth and RB's Yuki Tsunoda an impressive seventh for the Faenza-based Red Bull-owned team's home race.
Seven-time world champion Lewis Hamilton will start eighth for Mercedes and RB's Daniel Ricciardo ninth with Haas's Nico Hulkenberg completing the top 10 after giving Verstappen an aerodynamic tow in the final phase.
"He helped me out a few times in Q2 and I returned the favour. You need support sometimes," said the German.
Verstappen's Mexican team mate Sergio Perez, Verstappen's closest rival but 33 points behind, crashed in practice and will start 11th.
"I think we made some good progress with the car, like Max showed, but unfortunately from my side I didn't get to show it in Q3," he said.
Aston Martin won their race to repair Fernando Alonso's car in time for the session after the Spaniard also crashed in final practice but the double world champion made a ragged return and qualified 19th.
Williams's Logan Sargeant, whose place looks increasingly at risk, will start last.
