PHOTO: AFP
The 21-year-old Monegasque lapped the Baku street circuit with a benchmark time of one minute 41.604 seconds on a sunny afternoon.
Vettel, a four-times Formula One world champion, was 0.198 seconds slower. Red Bull's Max Verstappen ended the session a distant third and 1.248 seconds off Leclerc's pace.
Reigning champions Mercedes, who have scored one-two finishes in all of the season's three races so far, were fourth and fifth with Valtteri Bottas and last year's winner Lewis Hamilton respectively.
Bottas, robbed of victory in Baku a year ago by a blown tyre three laps from the end, was a tenth of a second quicker than championship-leading team mate Hamilton.
Russian Daniil Kvyat, who went into the wall on Friday, was an encouraging sixth for Toro Rosso. Denmark's Kevin Magnussen was seventh for Haas ahead of Kvyat's Thai team mate Alexander Albon.
Sergio Perez, the only driver to have stood twice on the Baku podium, was ninth for the Racing Point team with Alfa Romeo's Kimi Raikkonen completing the top 10.
Leclerc, who scored his first Formula One points last year with Sauber in Baku and in 2017 won a Formula Two race at the venue from pole position just days after his father's death, has been the man to beat all weekend.
Ordered to move over for Vettel in China and denied a maiden Formula One win by engine trouble in Bahrain, he was fastest in both Friday sessions.
The first practice was abandoned after 12 minutes when British rookie George Russell struck a loose manhole cover, wrecking his Williams.
There were no such dramas on Saturday afternoon however, with the session running incident-free and Russell back with a new chassis.
A few drivers, including Vettel, Hamilton and Bottas, ran wide off the track but resumed without incident.
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