In his first month as a starter, he registered five shutouts. He played 58 games and had a 1.95 average, the first goalie to finish below 2.00 since Bernie Parent was at 1.89 in 1973-74. Though little was expected from the Sabres after top scorer Pat LaFontaine had season-ending knee surgery in early December, Hasek led the Sabres into the postseason against the New Jersey Devils, where Hasek and the rookie Brodeur engaged in a terrific matchup, highlighted by a marathon Game 6 that extended into a fourth overtime before the Sabres prevailed 1-0. After six hours and 70 saves, Hasek said he felt he could have played two more periods. The Devils won Game 7, but in June, the 29-year-old Hasek won his first Vezina Trophy, was runner-up for the Hart Trophy and was on his way to superstardom.
More Vezina trophies and All-Star Team honors followed. Hasek starred at the 1998 Nagano Olympics for the gold medal-winning Czech Republic team and was named the tournament's top goalie. He then had a strong second half for Buffalo, helping the Sabres reach the Eastern Conference Final, and won his second Hart Trophy.
In 1999 he and the Sabres made it to the Cup Final against the Stars, who had Hasek's former teammate Belfour in goal. The series culminated in a three-overtime thriller in Game 6. Dallas won it 2-1 with one of the most controversial goals in Stanley Cup Playoff history. Hasek had made 50 saves, but couldn't make his 51st as Brett Hull banged in the puck around Hasek's net with his skate in the goal crease. Rules prohibited an attacking player from entering the crease before the puck, but the officials ruled the Stars had maintained possession of the puck prior to the shot and the goal was allowed to stand despite protests from Buffalo.