A hectic session was cut short after AlphaTauri’s Yuki Tsunoda and Ferrari’s Carlos Sainz crashed out in the final minutes to bring out the red flag for the fourth time.
Lance Stroll, Antonio Giovinazzi and Daniel Ricciardo had all also found the barriers earlier on.
And Verstappen was clearly seething that his rhythm was constantly being interrupted by crashes, having to settle for P3 with Mercedes’ Hamilton ahead of him and Leclerc on pole in the Ferrari.
The Red Bull driver leads Hamilton by four points in the Drivers’ Championship standings after winning the Monaco Grand Prix last time out and will bid to get past the Briton to preserve that advantage.
But speaking post-qualifying, a disgruntled Verstappen said: “It was a stupid qualifying to be honest. But anyway it is what it is. Still P3. We have a good car. Everything was working out fine.
“But yeah, all this s**t is all the time happening in Q3, I don’t care. It’s just unfortunate.
“It’s a street circuit so these things can happen. Our car’s strong so I just hope tomorrow in the race we can look after our tyres and score good points.
“We’re still up there. Of course I would’ve liked to start a bit further ahead but it’s still all to play for. Qualifying, a lot of things are happening.
“Maybe in the race these things can happen again. Let’s hope for a clean start and we’ll see from there.
“Yeah of course [it will be fun to battle Lewis]. Three different cars [at the front] as well. It’s always good to have that.”
Pole-sitter Leclerc declared: “It was quite a s**t lap I thought! There were two or three corners where I did mistakes but of course I had a big tow from Lewis in the last sector which helped me a little bit.
“Overall I think we would have been there or thereabouts for pole without the slipstream. It’s a good day. I didn’t expect to be as competitive as we were today.
“I was improving again before the red flag but it’s like this. Another pole, I’m happy anyway. Hopefully it’s all good for Carlos. I hope it’s all OK for the team.”
The Monegasque, robbed of starting his home race at the front of the pack a fortnight ago due to a mechanical issue, however expects a fierce test from Verstappen in particular.
He added: “The car felt quite OK but I believe Red Bull has something more than we have in the race especially. We’ve seen that in FP2 so it’s going to be very difficult.
“Here’s not like Monaco, they can overtake. We try to do the best job possible and hopefully we can keep first place. But it’s going to be difficult.”
Mercedes have struggled in Baku but Hamilton, who sandwiches Leclerc and Verstappen, is hopeful of an improved Sunday.
The reigning world champion said: “We definitely weren’t expecting that. This is such a monumental result for us. We’ve been struggling like you wouldn’t believe all weekend. You can see it.
“W We’ve moved around and made so many changes over these two days chasing our tail. It’s been so difficult. The work overnight and particularly between the sessions was amazing from the team.
“I’m really proud of everyone for keeping positive. To be up there and so close to these guys, it’s a great, great start.
“It’s been the biggest challenge we’ve had in a long time, trying to understand what the car really wants. She’s not been happy all weekend. It’s been a bit of a disaster.
“[But] Our race pace is a lot better than our single lap pace. We’re miles off in single laps and a lot closer in race pace. We don’t understand why.
“I’d like to think hopefully we’re in that same position so we can take the fight to these guys tomorrow.”