They had a score of 201.61 points to 200.46 by Canadians Marie-France Dubreuil and Patrice Lauzon.
Tanith Belbin and Ben Agosto of the United States were third with 195.43 points.
The top three were bunched within a half-point of each other entering the free dance.
Denkova and Staviski took the gold with a free dance program to a modern arrangement of Mozart's Requiem with a story theme of "Seven Deadly Sins" dressed in white.
At the end, Denkova was balanced on Staviski's knees in a routine full of intricate spins and rotations.
They have said this is their last competition and redeemed a third place finish at the European championships.
France's Isabelle Delobel and Olivier Schoenfelder, who won the Europeans, were fourth with Russians Oksana Domnina and Maxim Shabalin fifth, reports AP.
On Thursday, Brian Joubert became the first Frenchman in 42 years to win the world men's title while China's Shen Xue and Zhao Hongbo took the pairs event Tuesday.
The discovery of the submarine has unveiled a few "inconsistencies." For example, how can one explain the fact that the sub was found where it needed to be searched for from the start?
When on a state visit to Singapore, Russian President Vladimir Putin promised to revisit the discussion of the 1956 Declaration between the USSR and Japan regarding the issue of the peace treaty with Japan
The TurkStream, which runs along the bottom of the Black Sea from Russia's Anapa to Turkey, will consist of two lines, each with a capacity of 15.75 billion cubic meters of gas a year