Lance fought from the pitlane to gain nine positions en route to his top-10 finish while a late collision forced team-mate Sebastian Vettel to retire.
After securing 10th on the grid in Saturday's qualifying session, a pre-race fuel temperature issue forced Lance to start the Grand Prix from the pitlane.
By starting on the Hard tyre, the Canadian took advantage of the most durable compound to run long into the race and rise to a high of 10th position in the pit phase.
A collision between Pierre Gasly and Lando Norris, and a subsequent Virtual Safety Car and full Safety Car period, enabled Lance to pit for fresh tyres on lap 40 of 57.
Miami Grand Prix
Go inside the story of our 2022 Miami Grand Prix and hear from Lance, Sebastian and Team Principal Mike Krack. Discover the data underpinning our race and more in our comprehensive race report.
Swapping onto the mid-range Mediums and rejoining in 12th, Lance was pushed wide in Turn Two by Kevin Magnussen when the race was resumed at the end of lap 46.
This relegated him to 14th position before a collision between Sebastian and Haas's Mick Schumacher allowed Lance to regain his former position.
After taking the chequered flag, Lance was promoted to 10th post-race following a pair of penalties for Daniel Ricciardo and Fernando Alonso.
I think more points could have been on the table.
"Overall a frustrating afternoon. It was a shame to start from the pit lane but once the race was underway we showed some reasonable pace today," said Lance.
"It was quite difficult to overtake off-line, but we made good decisions and put ourselves in a position to finish inside the top 10 by pitting under the Safety Car.
"I think more points could have been on the table, but a bad restart and contact with Kevin [Magnussen] prevented that."
Sebastian faced a bitter end to the Miami Grand Prix and retired on lap 54 following a clash with Mick Schumacher when duelling for a place inside the top 10.
Facing the same pre-race fuel temperature issue as Lance, Sebastian also started the race from the pitlane and opted to run long in his first stint by utilising the durability of the Hard tyre.
By advancing through the field, he was on the verge of a top-10 breakthrough before a lock-up in Turn Seven on lap 36 demoted him to 15th.
Sebastian carefully avoided the lap 40 incident between Gasly and Norris to return to 13th, from where he boxed for new Mediums on lap 41.
It is a shame for this weekend to end in the way that it did and we should have done better.
He carefully avoided Lance's Turn Two clash with Magnussen on the lap 46 restart to advance to 12th and next cleared Alexander Albon for 11th.
After running in ninth for a brief moment, contact in Turn One with Schumacher halted his progress and forced Sebastian to retire.
"It is a shame for this weekend to end in the way that it did and we should have done better," commented Sebastian.
"We had a fuel temperature issue before the race which meant that we started from the pit lane.
"For the majority of the race I was stuck in traffic, it was quite difficult to overtake, and the DRS was not that effective.
"When the Safety Car was deployed, we moved into the top 10, but Mick [Schumacher] and I had contact, which cost both of us points."
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