Lance qualified ninth, and Sebastian was unlucky to miss out on Q3 at the last second, but a grid penalty elsewhere lifts both drivers up a place.
As a result, Lance will start the race in eighth and Sebastian will line up in 10th.
Lance and the Formula One field raced to make it onto the track as quickly as possible when Q1 went green because the threat of rain loomed.
Seeking to post a banker lap on Softs before the weather potentially turned, Lance's 1.44.856 lap time was representative of the challenging conditions.
While the track surface remained slippery, the rain held off, so Lance switched to another set of Soft tyres to seal his place in Q2.
He made the most of changing conditions and the new levels of grip following Istanbul Park's recent track improvements to find swathes of time.
Lapping in 1.25.511, Lance secured eighth and a Q2 berth.
In Q2, Lance, like the majority of the field, began the session on a set of new Medium tyres.
Lance fired in successive quick laps to end his first run in seventh after posting a 1.25.284 lap time.
Turkish Grand Prix
Get ready for this weekend's Turkish Grand Prix with our in-depth preview. Hear from Lance and Sebastian, and discover the key talking points for the race ahead.
A switch to new Medium tyres preceded a dramatic end to Q2 as the track surface significantly improved and drivers traded times and places on the leaderboard.
Lance rose above the battle after firing in a 1.24.601, which proved good enough for ninth, sealing a place in the top 10 battle.
Opting to conserve tyres, Lance began Q3 on a set of used Softs, meaning he ended the first runs in 10th courtesy of a 1.25.112 lap time.
With the benefit of a new set of Softs for his final run, Lance was able to easily improve on his earlier effort, leapfrogging AlphaTauri's Yuki Tsunoda for ninth after lapping in 1.24.305.
Lewis Hamilton will take a 10-place grid penalty for tomorrow's race, meaning Lance will start the Grand Prix in eighth.
"After practice yesterday, we made some helpful changes to the car overnight and I think that showed in our performance today," said Lance.
"Overall, I am satisfied and it was a good effort. I had a small off during my final run in Q2, but my previous lap was strong enough to make it into Q3.
"Tomorrow, we will be starting the race from eighth on the Medium tyre, which should put us in a good position for the opening stint.
"There are a few quick cars out of position on the grid – because of the conditions and various grid penalties – so we will have to capitalise on that, fight until the end, and push every lap to see where we end up."
Sebastian avoided the traffic ahead and rivals' mistakes to find a clear section of track for his first flying lap.
His AMR21 was fitted with the Soft compound, requiring precision on a damp track with spates of drizzle.
Sebastian's first effort of 1.26.889 put him comfortably inside the top 10 but drying conditions meant lap times quickly improved.
Extending his first stint to maximise the Istanbul Park track, the four-time World Champion was on the fringes of the top 10 midway through Q1.
Sebastian made sure of his place in Q2 late on with a final flying lap of 1.25.787 for 15th place.
In Q2, Sebastian looked to have sealed his place in Q3 in the final moments.
The German spent the early part of the session in sixth, lapping in 1.25.242 and just over four-thousandths of a second quicker than Lance.
He improved his time to 1.25.068 on his final lap on the Medium tyres before switching to another set of the mid-range compound.
A final effort of 1.24.795 looked set to reward Sebastian with 10th, despite damp sections of the track making it tricky to find a rhythm.
But Charles Leclerc used the tow from team-mate Carlos Sainz Jr to boost his run, knocking Sebastian out of contention.
While Sebastian was unable to take up the fight in Q3, he will start inside in the top 10 due to Hamilton's penalty.
"The conditions today were always improving and, although the track was mostly dry, there were still some damp areas where I struggled." said Sebastian.
"It was not easy to find a rhythm. I lost most of my lap time in those damp areas, especially in Turn One. After that, it was difficult to make up the deficit on the remainder of the lap.
"I think we had more pace in the car today so I am not happy to qualify 11th, but starting from 10th means we have a good opportunity to fight for points tomorrow."
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