The Finn lapped the six-km Baku street circuit in one minute, 40.495 seconds, just 0.059 seconds faster than team mate and championship leader Lewis Hamilton.
Red Bull's Max Verstappen celebrated his first Formula One pole position at the Hungarian Grand Prix on Saturday.
Daniel Ricciardo kept calm and carried on to win a tense Monaco Grand Prix for Red Bull on Sunday after power unit problems threatened to wreck his hopes of victory in Formula One's showcase race.
Lewis Hamilton won in Sunday's Azerbaijan Grand Prix ahead of Kimi Raikkonen and took championship lead.
Ferrari's new team principal Mattia Binotto said earlier in the year that Vettel, as the team's "champion", would be given priority over Leclerc in certain racing situations, though he later clarified the drivers would be "free to fight".
Formula One world champion Lewis Hamilton took pole position for the French Grand Prix on Saturday with Mercedes team mate Valtteri Bottas alongside him on the front row.
In a race of safety cars and surprises, Verstappen's former team mate Pierre Gasly made a first podium appearance in second place for Red Bull-owned Toro Rosso, a rare Honda-powered one-two.
Formula One breathed a sigh of relief on Sunday after the sport's new 'halo' head protection device saved Charles Leclerc from what might have been a potentially serious impact.
Ferrari's times were eye-catching, and quicker than anything from last year's weather-affected first four-day test at the Circuit de Catalunya.
Valtteri Bottas won the Azerbaijan Grand Prix on Sunday and retook the Formula One lead from team mate Lewis Hamilton after a fourth successive one-two finish for Mercedes.
Monaco's Leclerc, who had started on pole position for the first time, lost power with 10 laps to go while leading and finished third with an extra point for the fastest lap.
The Briton, who started his career working for the Hesketh team in 1977, died in Melbourne of a pulmonary embolism, it said.
Mercedes set for proper fight with Ferrari in Melbourne
Lewis Hamilton is hoping rain will come to the rescue as a Hockenheim heatwave threatens to dash Mercedes's hopes of a home German Grand Prix win on Sunday.
Lewis Hamilton's record already bears comparison to Michael Schumacher's, and in some areas exceeds the great German's achievements.
The win also set a record, one that Hamilton had previously shared with seven times champion Michael Schumacher, of 41 wins from pole position.
This year marks the first that two quadruple champions are competing in the same season and their battle to see who joins Argentine legend Juan Manuel Fangio in second place on the all-time list with five titles promises to light up the series.
Formula One's 'halo' head protection device makes its race debut this season in a 21-round championship with France and Germany back on the calendar and some new faces joining the old favourites on the starting grid.
Lewis Hamilton and Sebastian Vettel battle to match the late Argentine's 1950s feat of five world championships.
In an afternoon of heroes, Sebastian Vettel played the Bond villain at Silverstone, notes Raja Sen, who returns to Rediff.com as F1 columnist!
A summary of sports events and persons who made news on Wednesday
A summary of sports events and persons who made news on Saturday
'It was probably one of the most difficult decisions to take in my career so far. But I thought that it was time for me to take on a fresh and new challenge'
A summary of sports events and persons who made news on Tuesday
Lewis Hamilton was 'shocked' with the pace of Mercedes after notching a record-extending eighth pole position at the Australian Grand Prix ahead of team mate Valtteri Bottas as they thrashed their Formula One rivals in qualifying on Saturday.
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