Both Sarrou and Prevot managed to break away from the pack early and hold on to their leads, Ferrand-Prevot by a massive three-minute margin.
In the men's race, Sarrou won by 45 seconds from Swiss rider Mathias Flückiger who repeated his second place finish from 2019.
Third went to another Frenchman, Titouan Carod, 10 seconds further back.
Reigning Olympic champion Nino Schurter, bidding for his sixth consecutive XCO world title, was off the pace early and eventually finished ninth in windy conditions on a heavy, muddy course.
Pauline Ferrand-Prevot puts on a show
Eva Lechner claimed second in a thrilling photo-finish with Rebecca McConnell from Australia, 3:01 behind the winner.
McConnell looked safe for silver until a late crash allowed Lechner in with the Italian taking silver right on the line.
Prevot successfully defended her 2019 World title with a dominant ride, taking the lead from early on and never relinquishing first place, despite a couple of minor falls.
She became the first woman to retain the Elite Women Cross Country title at the UCI Mountain Bike World Championships since her French compatriot Julie Bresset in 2012-13.
She led by two minutes at the start of the third lap and never looked in danger.
It was a quieter victory than last year in the absence of the usual raucous crowd due to coronavirus, but there was no lack of excitement in the race with plenty of spills and thrills on the challenging course.
"I feel great," beamed Prevot post race.
"It was an amazing race and I wanted to have a good start because I knew that on the uphill and downhill it would be a bit hectic if I was in the group.
"I wanted to go solo but I didn't expect to have such a big gap so I tried to manage it and to give my best.
"It was good to have a good gap because of the possibility of a mechanical or a crash; something can always happen. I wanted to be safe until the end, and this way I could keep calm and ride a good pace.
"It's great to be able to defend the jersey," she continues, "and I'm super happy to ride another year with the world champion's jersey because I really like it. It's a good day for France, with the Under-23 women's title also for Loana Lecomte."
This is the French rider's third cross world crown, and she's keen to add an Olympic title at Tokyo 2020 next summer, erasing the memory of an injury-troubled Rio 2016.
Tough ride for Kate Courtney
2018 champion Kate Courtney failed to finish in Leogang.
It was a difficult race for the American who had a poor start with a mechanical stop on lap two of five ending her hopes of a return to the Worlds podium.
Sarrou seizes the day
It was a day to be out in front and out of trouble with multiple slips, skids, and falls.
In the early stages of the men's race, Dutch rider Milan Vader took the lead and was looking good until taking a tumble on a tricky descent before falling again shortly after.
Sarrou seized his chance and disappeared into the distance, while Schurter started poorly and dropped as low as 14th after the first lap.
The Swiss star recovered to take ninth but hands over the rainbow jersey for the first time since 2014.