Heading to Switzerland Olsson hadn't even managed a podium finish this campaign, his best finish being a sixth in Val di Fiemme in Italy.
But Olsson blew that out of the water in Davos as he crossed the finish line in 34:47.5 minutes for maximum points.
His nearest challenger and home favourite Dario Cologna was 11.8 seconds further back while Russian Alexander Legkov was third.
Despite winning the race Olsson is still some way out of the fight for medals in the overall World Cup standings as he sits 13th.
Meanwhile Cologna stretched his lead over Legkov by a further 20 points after beating him to the finish in Davos.
Cologan is atop the overall World Cup standings on 1173 points with Legkov second on 1034 with eight events still to go.