The McLaren driver came out on top of a thrilling battle between the pair, launching a move up the inside on lap 20 before spending the remainder of the 51-lap race keeping Leclerc at bay with some remarkable defending.
It secured the Australian his second Formula One win and helped move McLaren above Red Bull and into the lead of the constructors’ championship.
“I think for me it has to be one of the best races I’ve done,” Piastri said.
“It (the overtake) was a high-risk, high-commitment move but that’s what I needed to do to try and win the race because I wasn’t really going to be that keen to finish second. So I had to try.
“If I didn’t take that opportunity then I was never going to have another one I think. I mean credit to Charles. He was incredibly fair.
“I think maybe he thought I was going to sail on into the run-off but I was pleasantly surprised that I actually made the corner.
“The whole 30 laps where I was trying to keep Charles behind was incredibly tough.”
Piastri’s win capped off a fine day for McLaren as team-mate Lando Norris drove from 15th to fourth, overtaking title rival Max Verstappen in the closing stages.
Verstappen’s Red Bull team-mate Sergio Perez was on Piastri and Leclerc’s tail for the whole race but collided with Ferrari’s Carlos Sainz on the penultimate lap as both were eliminated.
McLaren now lead the constructors’ standings by 20 points.
Leclerc had stormed to pole for the fourth year in a row in Baku but he is still yet to win the race.
The Monegasque, who won Ferrari’s home race in Monza a fortnight ago, looked set to end that run when he pulled more than five seconds clear of Piastri.
But McLaren performed the undercut at the pit stops, putting Piastri on Leclerc’s tail – and his daring move was enough to take the lead.
“I was struggling on cold tyres and I thought it was not that much of a big deal if he overtook me because the race was still long and the DRS would help me,” Leclerc said.
“When my tyres got up to temperature I thought I would be able to overtake him but that was a misjudgement from my side.
“In these last two races, plus Singapore (next race), we need to maximise our opportunities to win races.
“Today I feel like we missed an opportunity.”
George Russell was handed a surprise podium for Mercedes when Perez and Sainz ended up in the wall – an incident for which neither driver was deemed to be at fault.
“We were fortunate to get onto the podium,” Russell admitted.
“We will take it. It is a good reward for all the efforts of the team after a challenging weekend on the whole.”
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