The 24-year-old Russian, seeded 10th in the championships, was run ragged in the opening set but drew on the experience of his 1996 French Open success to wear down his powerful opponent.
Kafelnikov said: "It's a great feeling to win this title as it is the last one of this century. Thomas made it very hard for me in the final but I just hung in there and hoped for the best."
And with reference to the absent world No 1 Pete Sampras, resting through fatigue, he joked: "I'd just like to thank Pete, wherever you are, for making this possible."
Enqvist went into this morning's final on the back of a 14-match winning run which had seen him take the Adelaide title and the Colonial Classic in Kooyong. And the unseeded Swede could also boast a 4-2 advantage over Kafelnikov from their previous encounters.
But the pressure of his first Grand Slam final proved too much for the world No 21 in front of a packed Flinders Park Centre Court crowd. He graciously paid tribute to his conqueror, saying: "First of all I must congratulate Yevgeny. He played too solid for me and is a worthy champion. Hopefully I can return here next year and go all the way."
Kafelnikov surrendered the first break of serve after a wild volley followed by a double-fault gifted the fifth game to Enqvist. Five games later Enqvist survived his first break point before a deep serve proved decisive on his fourth set point.
The second game of the second set saw a swing in momentum as a fierce return of serve from Kafelnikov helped him to a 2-0 lead after Enqvist had clawed back two break points from love-40. Enqvist lost his next service game to love after throwing away three of the four points with unforced errors. And another sloppy display in the sixth game helped Kafelnikov level the match with a whitewash.
Enqvist recovered his fighting spirit to take Kafelnikov to deuce five times before finally going 1-0 down in the third set. But his head was soon bowed again after a dubious line call at 30-40 helped the Russian double that advantage. Enqvist finally stopped the rot after nine games without a win and then amazingly recovered his first set zest to break back.
But his temperament again faltered in an erratic eighth game, whereas Kafelnikov held his nerve and his serve to take a two sets to one lead after surviving another break point.
The fourth set went comprehensively with serve, rounded off by Kafelnikov taking the 12th game to love. But the tie-break brought back all the demons of the second set for Enqvist as he fell tamely to a 5-0 deficit. He claimed one break back, but then lost the championship with a double-fault.Reuse content