Catsburg had started the sole Chevrolet Corvette C8.R from pole and maintained the lead at the start before making an early stop under the safety car.
But less than 90 minutes into the race, Catsburg was back in the pits with a front-right damper failure that took nearly 10 minutes to repair and dropped Catsburg, Nico Varrone and Ben Keating two laps behind the leaders.
Yet, despite the setback, the Corvette crew battled up the order, eventually gaining a lap back with a safety car pass around before some impressive pace from the trio returned them to the lead lap.
The C8.R briefly moved back into the lead in the 19th hour, eventually winning the class by a lap.
It marked Corvette's first win at Le Mans since 2015 and brought the curtain down on the GTE Am era at the 24 Hours.
"To be honest, no - I thought this is it," said Catsburg, when asked by Autosport if he thought any fightback was possible.
"We are two laps down and the race is going to be so long and I was pissed off with that.
"I thought I was going to have to drive for so long for nothing but somehow we made it back [to the front].
"We had great pace and with the safety car the way it is now, thank god, we got a lap back and the other lap we won back by just being faster than the others. It was insane we managed to get back."
Team-mate Keating had similar fears and at midnight - one third into the race - believed the best they could manage was seventh place.
He explained the changeable conditions during the night meant the team's plans "went out the window" and resulted in him driving both at night and in the rain, neither of which was originally intended for the bronze driver.
"The emotional rollercoaster was crazy," he said, when asked by Autosport about the turnaround in fortunes.
"I drove from 2am to 5am in the middle of the dark, knowing that my 51-year-old eyes don't see as well at night, knowing I would be giving up some pace to the Pros that were in the car at that time, but I've got to do what I can do to help the team. To have this result is incredible."
Keating added that the rate of attrition in the GTE Am field - just nine of the 21 starters were classified - shows how tricky the race was.
"You didn't have to have a failed damper for it to be difficult - it was difficult for everyone," he said. "But some of those difficulties are also what allowed us the opportunity to come back."
