Sebastian started 18th on the grid following a power unit-related penalty and made up eight places through a combination of strong wheel-to-wheel racing and good strategy.
Lance's race took an early setback due to contact at the first corner of the race, but he rallied to climb the order.
Sebastian started the race from 18th on the grid and was able to make up several places because of Nicholas Latifi's contact with Lance at Turn One.
Running in 16th through the high-speed Turns Two to Six, Sebastian soon cleared the Haas of Mick Schumacher in a strong set of opening laps.
By the time the first pitstop window opened, Sebastian had worked his way to 11th and the fringes of the points.
The four-time World Champion would run until lap 17 of 56 on used Medium tyres, pitting from eighth for a set of the same compound.
Uncover the story of the United States Grand Prix with our in-depth race report. Discover the data underpinning our race and hear from Lance, Sebastian and CEO & Team Principal Otmar Szafnauer as they review the Austin race.
"As we expected, it was a difficult race for everybody trying to manage the tyres with the hot track temperatures," said Sebastian.
"I was happy when everybody pitted quite early because we knew we would have a chance by running longer."
He would re-join the race at the rear end of a DRS train that spanned 15th to 10th and benefitted from a back-and-forth battle between Fernando Alonso and Antonio Giovinazzi to reel his rivals in.
At half-distance, Sebastian made his best move of the race by storming around the outside of George Russell through Turns 16 to 18 for 13th.
The second pitstop window soon opened, and the team's call meant Sebastian was able to make the most of fresher rubber compared to his rivals.
A final switch to a set of new Hard tyres gave Sebastian the platform to hunt down a points finish from 13th.
"It [the strategy] gave us fresher tyres at the end when it mattered, so we could move up into the top 10," Sebastian added.
"It was a good strategy by the team."
It was a good recovery after the grid penalty yesterday, and, when we were in clean air, the pace was good.
He quickly gained 12th when Alonso made his second stop and reeled Giovinazzi in, at times lapping one second quicker than the Alfa Romeo driver.
With five laps remaining, Sebastian used DRS to blast by Giovinazzi on the back straight to earn 11th.
And he then secured 10th and a point-finish when Kimi Räikkönen ran off track three laps from home.
"We only scored one point today, and we had to fight hard," said Sebastian.
"It was a good recovery after the grid penalty yesterday, and, when we were in clean air, the pace was good.
"With a couple more laps, we would have caught [Yuki] Tsunoda, but, from where we started, I think scoring a point is a good result."
Lance started the race from 13th on a set of new Medium tyres, but his chances of a points finish came to an end at the first corner.
As Lance turned into the left-hand Turn One, Nicholas Latifi hit the rear of the AMR21 and spun Lance around.
The Canadian dropped down to 19th and picked up damage that hampered his pace throughout the Grand Prix.
"I picked up a significant amount of damage on the front wing," said Lance. It cost us some performance, but we still managed to fight our way up the field."
Lance would spend his 18-lap first stint getting back in touch with the field before cycling his way up the order as his rivals pitted.
It's a race to forget, and we will move on and look to come back stronger in Mexico.
He demonstrated what could have been possible by dispatching both Haas drivers on the second lap and would pit from 10th for a set of the same compound.
Returning in 15th, Lance would also join the DRS train fighting for points, most notably duelling Alonso and Tsunoda in pursuit of the top 10.
Lance ran until the 34th lap before making his second stop and bolting on a set of Hard tyres for the final phase of the race.
Another battle with Alonso ended when Alonso suffered a technical issue and retired, while Raikkonen's late error helped promote Lance to 12th at the finish.
"It was not our weekend," reflected Lance.
"After yesterday's qualifying, where we were affected by the yellow flags, I was hit at Turn One on the very first lap today.
"It is a race to forget, and we will move on and look to come back stronger in Mexico."
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