The big favorite Pinturault - who climbed to the top of the podium in the combination in Sweden two years ago - had a golden position before the slalom in Italian Cortina.
The Frenchman was second after the super-G, eight hundredths behind the Canadian James Crawford.
Pinturault also took the lead easily when he went out as a second skier in the slalom, but the lead was short-lived.
The Swiss Marco Schwarz, fifth after the first run, 40 hundredths from the lead, is in dazzling slalom form and got a full hit.
He beat Pinturault by 36 hundredths and 4 hundredths in total.
It was Schwarz's first championship gold at senior level.
The 25-year-old already has an Olympic silver and a World Cup silver in teams.
He took World Cup bronze in slalom in Åre 2019.
Alexis Pinturault has won the combination cup six times in the last eight seasons and leads the overall world cup big.
He took the World Cup bronze in Thursday's super-G.