The Red Bull driver clinched victory in Baku after beating team-mate Sergio Perez, after Leclerc had retired with an engine problem on lap 20.
Leclerc had been leading the race at the time of his demise, having pitted before both Red Bulls under a virtual safety car.
Verstappen faced a 13-second deficit after his pitstop, but speaking after the race the Dutchman was confident he had the pace to overhaul Leclerc before the Ferrari's enforced retirement.
“I think today we had an incredible pace in the car, we could really look after the tyres and we could chip away at it, pass for the lead,” Verstappen said after securing his 25th F1 win over Perez by 20.8 seconds.
“But then, of course also, maybe a tiny bit lucky because with the retirement.
“But I think nevertheless, our car was really good today. So I could have closed that gap. Then of course you have a race on your hands.
“But overall, yeah, really, really happy with how the balance of the car was today.”
Verstappen also said he found a better set-up and tyre performance with his Red Bull in race trim, having struggled to match Perez over a single lap in qualifying and practice, which he said was key to his victory charge.
“I don't know, just tyre behaviour together with just general grip, of course, of the car,” he explained.
“And that's what you need around here, that you can look after your tyres. So at the end, to have a 1-2 as a team as well, it was a really good day for us.”
Coupled with Leclerc’s DNF, Verstappen now leads the world drivers’ championship by 21 points from Red Bull team-mate Perez as the Mexican moved up to second in the standings.
Having taken a maximum points haul in Baku courtesy of its 1-2 finish and Perez clinching the bonus point for the fastest lap, Red Bull extended its lead at the top of the F1 world constructors’ standings to 80 points over Ferrari.
