The 27-year-old from Sochi battled through a difficult first set before defeating Sargis Sargsian of Armenia, 7-6 (7-3), 6-2.
Kafelnikov reached the semifinals at the U.S. Open and the final at the President's Cup in Tashkent, Uzbekistan, winning his second title of the year at the Kremlin Cup in Moscow three weeks ago and advancing to the semifinals at Stuttgart.
His Moscow triumph was his fifth straight at that event, and he won this tournament in 1995 and reached the finals the following year. He was a semifinalist here last season.
The only other seeded player in action on Tuesday was No. 7 Greg Rusedski of Britain, who defeated Andrei Stoliarov of Russia, 6-1, 6-4.
Kafelnikov, defending champion Marat Safin and Germany's Tommy Haas are here looking to gain points toward clinching a spot for the Masters Cup in Sydney, Australia,
Safin, the third seed, reached the semifinals at the U.S. Open and claimed his first title of the year by beating Kafelnikov in the final at Tashkent. The Moscow native will try to avoid a three-match losing streak Wednesday when he faces David Prinosil of Germany.
Haas, seeded fourth, is coming off his biggest tournament victory of his career after winning at Stuttgart. He won his second title in a row, after capturing the CA Tennis Trophy in Vienna two weeks ago, and his third of the season.
Haas will play Andrei Medvedev of Ukraine in his opening match.
Five matches on Tuesday involved unseeded players.
Mikhail Youzhny of Russia defeated Alex Calatrava of Spain, 7-5, 7-5; Stefan Koubek of Austria topped Jiri Vanek of the Czech Republic, 6-1, 7-6 (7-0); Michael Llodra of France bested Dominik Hrbaty of Slovakia, 6-3, 7-6 (7-3); Felix Mantilla of Spain defeated Irakli Labadze of Georgia, 6-4, 7-6 (7-3); and Attila Savolt of Hungary topped Jacobo Diaz of Spain, 6-4, 7-5.
Notable deaths of 2014 [PHOTOS]