The world champion’s earlier fastest time had been beaten by Leclerc and his team-mate Carlos Sainz with their final laps but Verstappen snatched pole back.
The Dutchman was just 0.029 seconds quicker than Leclerc, with Sainz only 0.082secs off pole in a close session.
Both Mercedes crashed, leaving George Russell fifth and Lewis Hamilton 10th.
The session set the grid for Saturday’s sprint race, the result of which establishes the grid for the main grand prix on Sunday.
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Verstappen, who was serenaded by thousands of fans from his home country at his team’s home race, looked as if he had missed out as he headed into the final sector of his final lap.
At that point, he was not improving his time, and ahead of him on track Leclerc and Sainz were both doing so, and both slipped ahead of him.
But Verstappen was still pushing, and although he was slower than Leclerc through the final sector, he was quick enough along with his greater straight-line speed in the first sector, to grab pole back.
“In the end it was a really tight qualifying and it’s a really challenging track to get qualifying right,” said Verstappen.
On his hopes for the sprint, he added: “We have a great car. Hope it’s clean into Turn One and I get a good getaway. I feel confident with the car we have.”
Red Bull’s Sergio Perez completed the front two rows but is under investigation for exceeding track limits.
There are points available for the sprint – eight for the winner down to one for eighth place – and Leclerc really needs a good haul this weekend to revive his title hopes.
The Monegasque is 43 points behind Verstappen after a brutal run for him and Ferrari, in which he has lost potentially winning positions four times in five races through two engine failures and two strategy errors.
But Leclerc said only that he wanted a “clean race” after his difficult period.
“I struggled little bit with putting the tyres in the window after the red flag and this was enough give me some understeer and I struggle to drive around this whenever I have it,” said Leclerc.
“It is a shame but it is only Friday and looking at the last five races it is the Sunday that counts and I hope we can finally have a normal race.
“We just need a clean race and a good strategy on Sunday and everything is possible.”
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Hamilton had been looking competitive and was in contention for a place mixing it with the Red Bulls and Ferraris after setting third fastest time in the second part of qualifying, less than 0.2secs from pace-setter Leclerc.
But the seven-time champion made a most uncharacteristic mistake, losing control through Turn Seven on his first flying lap in the final part of qualifying.