The first two qualifying sessions included three red flags, and Lance Stroll sadly caused the first when he locked up at Turn 15 on his opening run in Q1, damaging the front-right of his AMR21.
Lance’s accident meant that the Formula One field had to return to the pitlane without setting flying laps.
Sebastian returned to the circuit on the same set of Soft tyres to post a 1.42.726 lap time to move sixth before the session was interrupted again.
Antonio Giovinazzi also hit the wall at Turn 15 and brought out the red flag moments later.
Sebastian was one of the few drivers to set a time in advance of the interruption but, on his second run, improved his best effort to 1.42.460 to take 10th in the final moments of the session.
Having underlined his potential Q3 pace in Q1, Q2 proved just as disruptive. Wanting to maximise track time in advance of any further red flags, Sebastian quickly took to the circuit.
He initially set a 1.42.224 lap time, which secured 10th at the end of the field's first runs, although he lost some time with a lock-up at Turn 15.
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Daniel Ricciardo's crash and subsequent red flag prevented Sebastian from completing a second run as the session was brought to a premature end with just over a minute left on the clock.
Cruelly, it meant Sebastian missed out on a Q3 place by three-thousandths of a second.
While disappointing, Sebastian will have the benefit of a free tyre choice to begin tomorrow’s Grand Prix.
Lance will start 19th, but the Baku City Circuit offers plenty of opportunities to make up ground in the race.
Sebastian: "We had good pace today. I was being patient and waiting to unleash the lap time at the right moment.
"Unfortunately, I took a bit too much risk on my best lap in Q2 and locked up going into Turn 15. I was lucky to continue, with a big flat spot, but it probably cost me about four tenths. That is what cost me a place in Q3.
"It is a tricky corner, downhill and bumpy, and it channels the wind. I am disappointed because we easily had the pace to go through to Q3.
"Then, with the early red flag, there was no opportunity to recover. Anyway, we are starting just outside of the points, but I think we can improve during the race with a nice rhythm and some good race pace."
Lance: "It was my mistake, and I have apologised to the team. Turn 15 is a challenging corner, as we have seen all weekend.
"It is off-camber and you brake over to the right, which means it is easy to lock up the front-right tyre under braking. With a tailwind like today, you can be caught out.
"I came into the corner too hot and locked up the tyre after I was already committed. I am obviously frustrated with myself, but the focus is on bouncing back tomorrow.
"You can overtake in Baku, so we will try to work our way up the field as much as we can in the race."
Otmar Szafnauer, CEO & Team Principal: "Sebastian was very unlucky not to have a chance to push for a Q3 place, denied that opportunity by Daniel’s [Ricciardo] Turn Three shunt with a couple of minutes of Q2 still to run.
"The session was then red-flagged, at which point Sebastian was 11th-quickest, just three-hundredths of a second shy of the Q2 cut-off.
"However, mitigating his ill fortune, he will start tomorrow’s race from P11, the best-placed runner able to select his own choice of tyres on which to begin the race.
"Lance hit the wall at Turn 15, sadly for us in Q1, which means that he will start the race from the 10th row.
"Points will be hard to get from back there, but you can be well sure that Lance will give it his all and, with a clever strategy and his strong race pace, points may be possible for him."
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