The paths of these two stars have intersected on several occasions due to their association with the luxury brand Bulgari
The Finn, who started from pole position for last year's race, edged out the six-time world champion, who is seeking a record-extending seventh win in his home event, by 0.138 seconds.
After Friday's extraordinary heat, conditions at the fourth Grand Prix of the 2020 season reverted to those of a more traditional British summer's day and saw the champion team return to their customary 1-2 positions.
Max Verstappen was third fastest for Red Bull, three-tenths off the pace, ahead of Friday's pace-setter Lance Stroll of Racing Point, Carlos Sainz of McLaren and Ferrari's Charles Leclerc.
Lando Norris was seventh in the second McLaren ahead of Daniel Ricciardo, running a new Renault chassis, Nico Hulkenberg who is replacing coronavirus victim Sergio Perez in the second Racing Point and Pierre Gasly of Alpha Tauri.
On a notably cooler and overcast morning, the air temperature having fallen from 35 degrees Celsius to 19, Vettel was first out in his Ferrari before his lap time was trimmed by his 2021 successor Sainz.
In the much-changed conditions, with a switch in wind direction too, car behaviour and performance had altered significantly and it was not long before Mercedes found their rhythm.
The champions had struggled in Friday's sweltering heat, but 20 minutes into FP3 they were back on top with Bottas and then Hamilton leading the way, both lapping inside Stroll's best time from the opening day.
Bottas responded to his team-mate with 15 minutes to go when he lapped in 1:25.873 shortly before Alexander Albon finally made it out on track in the final flurry of action, but ran off track briefly.
Albon, the London-born Thai driver who crashed heavily on Friday, had suffered a further setback when his newly-repaired Red Bull was detained for electrical system refinements.
The paths of these two stars have intersected on several occasions due to their association with the luxury brand Bulgari
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