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.

Volkov won the Kremlin Cup a year later in 1994 to claim his third (and final) career title.

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.