Four-time champion Sebastian Vettel took second for Aston Martin after an impressive drive after qualifying 11th. Pierre Gasly was third for AlphaTauri.
Mercedes driver Lewis Hamilton and his Red Bull rival Max Verstappen would like to see team bosses Toto Wolff and Christian Horner don boxing gloves to settle their differences.
Leclerc set his time of 1 minute, 41.218 seconds early in Saturday's third session.
AlphaTauri's Gasly was fastest in a time of 1 minute, 42.251 seconds, beating Perez by .344 seconds.
Perez set a time of 1 minute, 42.115 seconds in the second practice to lead Verstappen by .101 after the Dutch driver had been fastest in the first session.
The race, which is held on a windy street circuit through the city, was one of several canceled last year because of the pandemic.
The race at the Baku City Circuit was scheduled for June 7 but has been called off after discussions between governing body FIA and the local government.
That was the fourth straight one-two finish for Mercedes, the best start to a season by a two-car team in Formula One history.
The Azerbaijan street circuit was widely considered an unlikely F1 host when it held its first race in 2016 but has won popularity with fans after some unpredictable races.
Ferrari's Kimi Raikkonen claimed second place after having dropped to 14th following an early collision.
Sebastian Vettel qualified in pole position on Saturday for the third straight time this season ahead of the Azerbaijan Grand Prix.
Ferrari's Vettel had lacked pace on Friday on a slippery track but was 0.361 seconds faster than the second-place Mercedes of Lewis Hamilton — his main title rival — in cool, overcast conditions.
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