The new-look format reduced practice down to a single hour before qualifying, as opposed to the usual three one-hour sessions.
The two drivers made the most of the hour to complete running on the Soft, Medium and Hard tyre to help set a baseline for qualifying.
Sebastian ended free practice one in seventh after posting a 1.28.062 lap time, while Lance finished 18th after he was unable to maximise the soft tyre late on, lapping in 1.29.597.
They then took on the challenge of a Friday night qualifying to set the grid for tomorrow's Sprint race, which, in turn, will decide the Grand Prix starting order.
As a result of the new format, Sebastian and the rest of the field used Soft tyres exclusively in qualifying.
Sebastian immediately demonstrated his top 10 pace with a 1.28.327 lap time right out of the box, and it became clear that track evolution was playing a key role in the placings, meaning the second run was critical.
The German rose to the occasion by taking 10th in the final moments of the session after lapping in 1.27.493.
He continued where he left off in Q2 and managed to save a second set of Soft tyres by posting a strong effort on his first run.
A 1.27.103 lap placed Sebastian fifth early in the session, and the time proved a significant buffer that allowed him to remain in the garage.
British Grand Prix
Get ready for this weekend's British Grand Prix with our in-depth preview. Hear from Lance and Sebastian, and discover the key talking points for the race ahead.
A flurry of late improvements meant Sebastian ended Q2 in eighth after just three laps of the Silverstone circuit.
In Q3, Sebastian was unfortunate to have his first lap time deleted, which put the onus on his final flying effort.
He would qualify 10th for the first-ever Sprint race courtesy of a 1.27.129 lap, affected by minor time loss at a couple of corners.
With a 17-lap race deciding the grid for the British Grand Prix, Sebastian is targeting a good result on Saturday to set him up strongly for the Grand Prix.
"I would have liked to end Q3 higher up because the car has looked competitive and the pace came quite easily today.
"Overall, it was a decent session: I was happy with my best lap in Q2, but in Q3 I struggled to find more from the car. So I think we could have been a few places higher up.
"It was great to see the big crowd here today and I guess the new format made Friday more interesting for the fans."
Lance and the team worked between FP1 and qualifying to improve the balance of the AMR21 and the Canadian progressively improved throughout Q1.
On his first run, Lance lapped in 1.28.917 before a switch to a new set of Softs yielded a quicker 1.28.017 lap time that secured a Q2 berth.
Technical difficulties required set-up changes to Lance's AMR21, which impacted his Q2 efforts, but Lance battled until the end of the session in a bid to make Q3.
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His first lap time of 1.27.823 was initially within the top 10 but a series of quick lap times across the field led to a tense shootout.
Despite finding more time on his second run, he suffered oversteer at Maggotts and Becketts, which meant he could only qualify 15th.
With the potential to make up places in tomorrow's Sprint race, Lance aims to move closer to the top 10 on Saturday ahead of the Grand Prix finale.
"P15 is not how we wanted to start our home event, but there is an opportunity to improve tomorrow thanks to the Sprint Race format.
"I was not totally comfortable in the car during practice, but I think we made some progress in qualifying, although it was not enough to make Q3.
"It was a challenge to only have one practice session today before qualifying, but it is the same for everyone.
"We will go away tonight and learn from today to make sure we maximise the second practice session before Sprint Qualifying."
Otmar Szafnauer, CEO & Team Principal
"We had some technical difficulties with Lance's car in Q1, which necessitated our having to make some changes to it for Q2.
"He did his best with that new set-up in Q2, but he was hampered by oversteer at Maggotts and Becketts, as a result of which he was not able to progress to Q3.
"Sebastian was happier with his car and, benefiting from a few tenths advantage of a fresh engine, duly made it through to Q3, although on his best Q3 lap he lost a small amount of time at Turns Six and Seven, and Turns 11 and 12.
"But what matters most now is converting today's results into as good a performance as possible in tomorrow’s Sprint Race Qualifying, so as to optimise our chances of scoring solid points in Sunday's feature race."
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