Volkov finished runner-up in three tournaments over 1989 and 1990; in the latter year he defeated World No. 1
Stefan Edberg in straight sets in the first round of the
US Open. Volkov won his first top-level professional singles title in 1991 at
Milan. At
Wimbledon that year, he lost a close match in the fourth round to the eventual tournament champion
Michael Stich, 4–6, 6–3, 7–5, 1–6, 7–5 despite winning the same number of games as Stich overall in the match, which hinged on a lucky shot hit by the German when he was trailing 4–5 in the final set. With Volkov serving for the match, at 5-4 and 30–30, Stich hit a seemingly-wide shot that caught the net and, instead of going out, looped over Volkov's head and back into play for a winner. What could have been 40-30, and match-point for Volkov, instead became a vital break-point opportunity for Stich at 30-40, that he immediately converted. Stich subsequently won the next two games and the match. Volkov was runner-up in three tournaments in 1992 and won his second title in 1993 in
Auckland. Later in 1993, Volkov defeated
Björn Borg in the first round of the
Kremlin Cup in
Moscow, in a match which proved to be the last of Borg's career. Volkov won the Kremlin Cup a year later in 1994 to claim his third (and final) career title. He reached one more final in 1997 in Shanghai. His best Grand Slam singles performance was reaching the semifinals of the
1993 US Open, where he defeated
Jonathan Stark,
Kevin Ullyett,
Amos Mansdorf,
Chuck Adams and
Thomas Muster before losing to
Pete Sampras. Volkov was part of the Russian team that reached the final of the
Davis Cup in 1994. He won singles rubbers over
Patrick Rafter of
Australia in the first round and
Michael Stich of
Germany in the semifinals. However, he lost both his singles rubbers in the final as Russia was defeated by
Sweden 4–1. Volkov retired from the professional tour in 1998. His career-high singles ranking was world No. 14 in 1994. His career prize-money earnings totalled
$3,362,786. He was
Marat Safin's coach before the duo split in July 2007. ==ATP career finals==