Both drivers survived contact and were able to gain positions while also showing great pace in the race.
Sebastian came on strong late on to just miss out on ninth place but picked up a point, while Lance had a good chance of a points finish ruined after contact with Daniel Ricciardo.
Starting on a fresh set of Soft tyres, Sebastian was able to hold position at the start despite minor contact in the opening corners and then climbed a couple of places as drivers pitted early with damage.
He then worked his way past Yuki Tsunoda, and pitted on lap 15 in response to the AlphaTauri driver's stop.
From there, he worked his way past Alex Albon and the one-stopping Alpine duo of Fernando Alonso and Esteban Ocon (who were struggling on Hard tyres) before his second stop.
Charging into the points at the Hungaroring
Sebastian led Lance to bring home a hard-earned point for the team in the final race before the summer break as both drivers climbed up the order at the twisty Hungaroring.
Sebastian switched onto the Medium tyre on lap 46 in a well-executed double-stack by the team and returned to the track in 13th.
From there, he passed Daniel Ricciardo and Valtteri Bottas (who was also on a one-stop) before switching positions with Lance in an attempt to catch Ocon.
A Virtual Safety Car late in the race for Bottas stopping hindered Sebastian's chances of the extra point, and he came up short by 0.143 of a second.
Regardless, he came home in 10th to bring home a valuable point for the team.
We ran out of time. I was very close on the final lap, but I needed just one more corner to make a move.
"We had to fight hard for a point today and we came close to a second point when I was chasing down Esteban in the final laps.
"The team switched cars because I had a better opportunity to catch Esteban, but obviously the Virtual Safety Car hurt us and we ran out of time. I was very close on the final lap, but I needed just one more corner to make a move.
"Overall, it was a fun race with lots of fights and overtakes. The middle stint was a bit difficult, but the balance was better for the third stint on the Mediums.
"The race pace was competitive, once again, so improving our Saturday performance needs to be a focus for the second half of the year."
Lance started the race on the Soft tyre and held position at the start, but gained a position early on as Kevin Magnussen pitted for damage.
He pitted on lap 14 and switched to the Medium tyre. With his fresh rubber, he was able to catch and pass Albon, before passing the Alpine duo of Alonso and Ocon.
He was closing in considerably on Ricciardo and both pitted on lap 46. Lance was then hit into a spin by Ricciardo when they were battling at Turn Two, for which the McLaren driver picked up a five-second penalty.
I gave Daniel room on the inside at Turn Two, but I think he was struggling for grip on the Hard tyre and went a bit too deep.
Despite this, he caught and passed Zhou Guanyu and Ricciardo before taking huge chunks of time out of the 13-second gap to Bottas.
He passed Bottas, but with tyre performance dropping off he switched positions with Sebastian and finished in 11th position.
"I think I drove a strong race today. Into the final stint, Sebastian was on the Medium and I was on the Soft – I did not have another Medium left, and he could make that tyre last a little bit longer.
"The Soft was the wrong tyre in the circumstances, sadly, but these things happen in racing. I had fun racing into the top 10.
"When I came up to pass Daniel, I gave him room on the inside at Turn Two, but I think he was struggling for grip on the Hard tyre and went a bit too deep. That is how it goes sometimes.
"We seem to have better pace on Sundays than we do on Saturdays, so we need to look at that. But there are plenty of positives to take away from today."
All in. All welcome. All celebrated. Sign up to open up a world of I / AM benefits and once-in-a-lifetime experiences.