Vingegaard crossed the line 42 seconds ahead of Martínez which was enough to put him in the leader's yellow jersey.
The Danish rider took over the lead from Juan Ayuso, who along with a number of riders was involved in a crash with 46km to go, and was forced to abandon.
Red Bull-Bora-hansgrohe held all the cards to steal the stage win on the final climb up to the finish in Uchon, with Mick and Tim van Dijke working hard to drag team-mate Martínez the whole way up the 8km ascent, while Vingegaard was comfortable sitting in fourth wheel.
However, in the decisive phase Martínez had no answer when Vingegaard pulled away shortly before the finish to claim an accomplished victory.
For many riders the only objective was focused around just being able to finish the stage as a bitterly cold, rainy day through the hills of central France tested the riders to the maximum as the main peloton with Ayuso, Vingegaard and Martínez was shattered into pieces long before the final climbs and the mass crash.
Ineos Grenadiers co-leader Kévin Vauquelin, who was in third spot overall was dropped early, while teammate Oscar Onley who was second also suffered a cruel fate when he suffered an early fall followed by a mechanical and finished more than three minutes down.
However, the real chaos began during a big pile-up at 55 kilometres during a sweeping descent that saw Ayuso fall heavily and abandon, whilst other top contenders like Brandon McNulty (UAE Team Emirates-XRG) and Spanish National Iván Romeo (Movistar) also couldn't continue the race.