From the outset, experts say Carlsen is favored to win, but Karyaking continues to frustrate him in difficult positions.
However, during the last two matches held Friday and Sunday, Karyakin was unable to capitalize on his advantage.
"The last two games have not been so interesting," Carlsen said Sunday, but, he added: "anything can still happen. We have now a five-game match."
The tournament is being followed in-person by hundreds of fans, many of whom have traveled to New York specially for the matches, while tens of thousands of fans follow the latest developments online on chess sites such as chess.com and chessbase.com.
With every draw, the players earn 0.5 points, meaning after seven draws Carlsen and Karyakin each have 3.5 points.
A victory is worth 1.0 point.
The first to reach 6.5 points will be declared world champion and will take home 600,000 euros. The loser will walk away with a consolation prize of 400,000 euros.
If there is still a tie after the 12th game on November 30, new matches will be scheduled.
It is the first between players who came of age in the computer era, representing a generational shift in the game.
Carsen is 25 and Karyakin 26, and with their ages combined, they play the youngest chess world championship ever.
The battle has prompted comparisons with the 1972 showdown between American Bobby Fischer and the Soviet Union's Boris Spassky, two rivals in the Cold War-era whose showdown was dubbed the "Match of the Century."