The No.11 player in the world and third seed in the tournament faced match point on Haarhuis' serve at 5-4 in the second set, but came back to triumph, 4-6, 7-5, 6-1, delighting the home crowd at Moscow's Olympic Sports Center.
"I felt I would lose the match, I was sure," Kafelnikov said afterward.
"At that point I decided I was just going to play my best, and that's why I won," he said, adding emphatically that "the spectators helped me greatly."
Certainly, if the crowd had cheered for the underdogs who had knocked out top seeds Sergi Bruguera of Spain and Todd Martin of the U.S. on Wednesday, it wanted no such fate for its countrymen against Haarhuis, ranked 39th in the world.
Hush silences fell when Kafelnikov's serve was broken, and applause erupted when the Russian eked out key points.
A blistering two-handed backhand handcuffed Haarhuis at net at the 40-30 match point, and Kafelnikov quickly won the game, held his serve and earned the break to win the second set, 7-5.
Buoyed, Kafelnikov in the third set began hitting his ground strokes and serves with more authority, flattening out his forehand and finding the baseline corners with uncanny precision. In gaining the key break in the second game of the third set, Kafelnikov left his opponent frozen with a thundering forehand return of service to the near corner to go up 2-0.
Kafelnikov cruised the rest of the way, closing up the match with an ace and then booming a ball into the stands to celebrate.
After the match, a relaxed Kafelnikov said comments he made Tuesday that he might not play for Russia in the Davis Cup final against Sweden next month because of differences with the team captain, had been misunderstood.
He will be in the line up for the home match Dec. 2 to 4, he said.
Kafelnikov next faces sixth seed Marc Rosset of Switzerland, who advanced Thursday with a 6-4, 6-2 win over Markus Zoecke of Germany.
In other matches Thursday, Karol Kucera fell to Haarhuis' Dutch doubles partner Jacco Eltingh, 6-4, 3-6, 7-6 (7-2), one day after the Czech had ousted world No.5 Bruguera.
Eltingh will face No.7 seed Petr Korda, who also was taken to three sets Thursday, but held off Alexander Mronz of Germany, 4-6, 7-5, 6-3.
In the other round of eight pairing, Carl-Uwe Steeb of Germany will take on Chuck Adams of the United States who knocked off second seed and world No.10 Martin in the second round Wednesday.
Russia's Alexander Volkov advanced to the quarters after his opponent, Daniel Vasek of the Czech Republic, unfortunately withdrew with a leg injury.
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