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 United States' Head of Diplomacy, or Secretary of State, is an anachronistic, incompetent, meddling, intrusive, insolent and arrogant, rude individual, a brash, foul-mouthed upstart, a conceited, self-important guttersnipe and an insult to the international community, as fit for the job as a pedophile janitor in a grade school.