The individual event at the Race of Champions was won by Mattias Ekstrom, a rallycross driver who has now won the Champion of Champions four times.
Schumacher battled past Felix Rosenqvist, the IndyCar driver, in the first preliminary round.
Meanwhile, David Coulthard spun out early and Mika Hakkinen was eliminated by Felipe Drugovich.
Valtteri Bottas was beaten by Tom Kristensen, the Le Mans legend, after a five-second penalty.
Vettel edged past Jamie Chadwick, the three-time W Series champion, in both heats.
Schumacher then eliminated Drugovich despite running off track in the final moments of their second heat.
Vettel beat Kristensen, but then lost out to his friend Schumacher in the semi-final.
Schumacher had a 10-second lead after Vettel ran off track and needed to go through a snow barrier.
But the ex-Haas F1 driver lost out to Ekstrom in a best-of-three final.
False start cost Schumacher and Vettel
In the Nations Cup event, pitting pairs of nationalities against each other, Team Germany (Schumacher and Vettel) lost out after a false start.
Vettel incurred a five-second penalty which cost his team against Brazil’s Drugovich.
Schumacher couldn’t beat Thierry Neuville, meaning Team Germany were sent packing.
The Germans had previously beaten Team GB (David Coulthard and Jamie Chadwick).
Father-son duo of Petter and Oliver Solberg (Team Norway) won the Nations Cup.
