Aston Martin, formerly known as Racing Point, currently sit seventh in the constructors' championship, with Vettel recording their best result — finishing second in Azerbaijan.
Formula 1 2021: Red Bull's Max Verstappen clocks fastest lap in Belgian Grand Prix practice before crashing
The Dutchman had set a best lap in one minute and 44.472 seconds to outpace Valtteri Bottas by 0.041 seconds and championship leader and seven-time champion Lewis Hamilton by 0.072 seconds before he ended the session after hitting the barriers at Malmedy.
The 33-year-old German has never won a Grand Prix, but proved himself a valuable asset when standing in for Covid-19 casualties last season, before it rebranded as Aston Martin.
The four-time world champion Vettel, who joined the Aston Villa team this year after leaving Ferrari, failed to make the cut from Q1 and struggled to make an impression.
Vettel considered retiring but a move to Aston Martin has rekindled the 33-year-old German driver's enthusiasm.
Formula 1 2021: Sebastian Vettel targets another world title as Aston Martin unveil car in return to sport
"I think I have another world championship in me... I am not too old and I still have a long time in me," said new Aston Martin driver Sebastian Vettel, who spent six luckless campaigns with Ferrari.
Formula 1 2020: Racing Point's Sergio Perez bids tearful farewell after engine failure wrecks Abu Dhabi GP
"It is sad to be leaving the team this way," said Perez, who said he retained hopes of staying in Formula One with Red Bull, if they chose him as a replacement for Alex Albon.
On his final lap, slowing down round the Yas Marina Circuit, Vettel surprised many by singing an Italian song about Ferrari on the team radio system.
Perez, who has been at Racing Point, previously known as Force India, since 2014, is to be replaced next year, when the team is re-branded as Aston Martin, by four-time world champion Sebastian Vettel.
The Racing Point driver finished 10.5 seconds ahead of Renault's Esteban Ocon and 11.9 clear of teammate Lance Stroll.
Formula 1 2020: Red Bull sporting director Jonathan Wheatley to miss Bahrain GP after testing positive for COVID-19
The vastly-experienced key pit-wall decision-maker returned a positive test during mandatory pre-race tests and will be isolation for 10-days in line with the sport’s protocols and public health guidelines.
Defending six-time champion Hamilton, who bids to capture a record-equalling seventh world title in Sunday's race, was only sixth in qualifying with his teammate Valtteri Bottas in ninth.
For Racing Point's Lance Stroll, this was the first pole position of his Formula One career. His teammate Sergio Perez was third.
French driver Pierre Gasly's car caught fire on Friday while there was a crash between Red Bull's Max Verstappen and Lance Stroll's Racing Point car.
Formula 1 has revised COVID-19 testing protocols after Lance Stroll case, says Racing Point boss Otmar Szafnauer
Canadian Stroll, 21, left the Eifel event early on Sunday, flying home to Switzerland, where he returned a positive test result on Monday.
Lewis Hamilton and Mercedes seek to continue their record-making progress as Formula One escapes in search of some autumnal sunshine at this weekend's Portuguese Grand Prix.
Formula 1 2020: Racing Point driver Lance Stroll intent on competing at Portuguese GP following week of self-isolation
In a post on Instagram, Stroll said he spent 10 days at home in self-isolation with mild symptoms and returned a negative test on Monday.
"I don’t think we need to be in on Fridays," said Lewis Hamilton.
Hamilton briefly sat atop the time charts, but his Mercedes teammate Bottas sped through seconds later with an unbeatable time, fastest in all three sectors of the Nürburgring track.
It was not made clear if Stroll had tested positive for COVID-19. But Stroll's teammate Sergio Perez after returning from Mexico and testing positive for the coronavirus ahead of the British Grand Prix in July.