Lance finished 10th on the road at the end of the 18-lap race, two places ahead of team-mate Sebastian, who will start Sunday's race in 11th after Valtteri Bottas takes up his back-of-the-grid starting position.
The field was split on whether to complete the Sprint on Soft or Medium tyres, and the team opted for Softs on both cars.
Lance launched strongly off the line and raced alongside Sebastian and Red Bull’s Sergio Perez into the opening chicane.
Taking the wider line through Turns One and Two, Lance moved up to 10th at the exit, which swiftly became ninth following an incident for AlphaTauri's Pierre Gasly.
A three-lap Safety Car followed while the AlphaTauri was recovered.
Lance came under pressure from Perez, but smart defensive driving kept him ninth until midway through the race.
Perez launched an ambitious move at Turn One that forced him to take the escape road, but the Red Bull driver rejoined in front of Lance.
The Red Bull driver took until the Ascari chicane to hand the position back to Lance, affecting the Canadian's race and putting him under pressure from Alpine's Fernando Alonso.
While Perez would eventually get past, Lance held onto finish the Sprint in 10th, making impressive ground in the short race.
Italian Grand Prix
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"That was a fun race today. It was not an easy decision to go for the soft tyre over the medium because, while it provides a better launch, degradation becomes a factor later on.
"We made a good start and gained some places in what was quite a tricky first chicane with all the tyre smoke and loose grass.
"I then had some good wheel-to-wheel racing with Checo [Perez] later on, too. He gave the position back to me a little later than I expected, which lost our DRS train and allowed [Fernando] Alonso to close in, but we were able to hold onto 10th.
"We will start tomorrow's race in the mix for points and I think we can extract a little bit more pace from the car overnight.
"Overtaking is tricky here so strategy will be important, but I am looking forward to racing again tomorrow."
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Sebastian battled hard at the beginning of the race and exited the opening chicane in 11th after battling Lance and Perez.
He then took part in an exciting back-and-forth with Alonso down the start/finish line and was able to hold onto his place until the Spaniard darted past at Lesmos on lap four.
Sebastian then battled Alonso's team-mate, Esteban Ocon, across the remainder of the race, and expert defending allowed him to hold onto 12th.
Like Lance, Sebastian gains a place on the grid due to Bottas’s penalty, meaning he lines up 11th for tomorrow's race.
"It was a tricky race for me. I made a good start off the line, but I had nowhere to go in the packed field of cars so I locked up into Turn One.
"As a result, I had significant flat spots on the front left and right tyre, which created a lot of vibration. It became a race of damage limitation.
"We will start in a similar position in tomorrow’s race to where we did today. As we saw this afternoon, overtaking can be difficult because it is hard to follow the car in front, but we will see what we can do and try to fight for points."
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