Svendsen and the Frenchman reached the final straight together but the Norwegian seemed to have sealed victory when he pulled away in the sprint for the line.
But Fourcade fought back to lunge towards the finish - the first binding to cross the line determining the winner - just as Svendsen raised his arms in celebration.
The official television feed initially showed Fourcade, who had earlier claimed the 20km individual and 12.5km pursuit titles, as the winner.
A photo finish was called and Svendsen, who had disappointed in the first three races here, was awarded the victory after his 20km individual and relay golds in Vancouver in 2010.
Czech Ondrej Moravec took the bronze in a race that had been postponed twice because of fog.
Norwegian Ole Einar Bjoerndalen missed out on a record 13th Winter Games medal when he made two mistakes at the final shooting and finished 22nd.
The start was delayed by 15 minutes because of snow before Fourcade and Bjoerndalen made one and two mistakes respectively on the first shooting.
Bjoerndalen made huge efforts to catch the leading group, which he paid for at the final standing shooting.
(Reporting by Julien Pretot; Editing by Robert Woodward)
