The race, which had been repeatedly postponed due to bad weather, was run in a swirling wet snow, which provided a suitable backdrop to the dramatic scenes.
Svendsen slowed up as he raised his hands in victory just before crossing the line but he had apparently failed to notice Fourcade, who flung himself across the finish.
Both were given the same time of 42min 29.1sec but Svendsen, who will count himself lucky, was awarded the gold by a whisker on the photo. Fourcade was aiming for his third gold at Sochi after winning the pursuit and the individual.
Ondrej Moravec of the Czech Republic took the bronze.
Norway's Ole Einar Bjoerndalen, seeking a record 13th medal at Winter Olympic Games, will have to wait until the relays after coming 22nd following a nightmare four missed targets on his final standing shooting.