That season, Scott became the youngest player to play for the Devils and played four games (one assist) before returning to junior for the rest of the season. In 1992-93, Scott joined the Devils full-time and was an NHL All-Rookie Team defenceman. In 1993-94, Scott finished third on the Devils with a +34 rating and led the team to their its ever 100-point season in the standings. In the playoffs, the Devils pushed through to the Eastern Conference final before bowing out to the eventual Cup winners, the Rangers. In the shortened 1994-95 campaign, Scott led the Devils with a +19 rating; in the playoffs, he led all Devils' defencemen with 11 points. In the 1995 Stanley Cup final, Scott scored a beautiful goal off an end-to-end rush in Game Two of the Devils' four-game sweep for the title.

After missing the playoffs in 1995-96 (Scott led the Devils' defence with 179 shots), Scott and the Devils posted the league's stingiest defence in 1996-97 and won the Eastern Conference and Atlantic Division regular season titles with 104 points. That year, he led the Devils with 18 power play points. In 1997-98, Scott and the Devils again allowed the fewest goals in the league and again won both the Eastern Conference and Atlantic Division season titles. The Devils' 48 wins and 107 points were both franchise records. That year, Scott participated in his first midseason All-Star Game, was a year-end Second Team All-Star and led the Devils with 43 assists, 11 power-play goals and 29 power play points. In 1998-99, Scott led all team defencemen with 46 points as the Devils posted their third consecutive 100-point season (105) for both the Eastern Conference and Atlantic Division season titles.

In 1999-2000, Scott led team defencemen in scoring for the fifth straight season (38 points) and the Devils won more than 100 points (103) for the fourth straight year. In the playoffs, Scott led the Devils to their second Stanley Cup championship. In 2000-01, Scott led the Devils to an Atlantic Division title with a club record of 48 wins (tied) and 111 points. After missing the start of the season, Scott played in his second mid-season All-Star Game and finished the year with 35 points in 57 games. In the playoffs, the Devils won the Prince of Wales Trophy before losing to the Avalanche in the Stanley Cup final.

In 2001-02, Scott scored 33 points in 76 games as the Devils dropped 16 points in the standings to finish third in the Atlantic Division. In the playoffs, Scott scored two assists in six games as the Devils lost in the opening round to the Hurricanes.

In 2002-03, Scott played 81 games and scored 39 points. He led all team defencemen with 11 goals and co-led the team with a +23 plus/minus rating. The Devils, meanwhile, bounced back 13 points in the standings to win their fifth Atlantic Division title in seven years. In the playoffs, Scott first helped the Devils win the Prince of Wales Trophy by knocking off the Bruins, the Lightning, and the Senators. The Devils then defeated the Mighty Ducks to win their third Stanley Cup championship.

In 2003-04, Scott finished tied for second amongst all league defencemen with 40 assists and 54 points. He co-led the Devils with nine power-play goals as the team won more than 40 games for the eighth-straight season. In the mid-season All-Star Game, he scored an assist for the winning Eastern Conference squad (6-4). On March 23, he scored the overtime game-winning goal to earn Martin Brodeur his 400th career win. In the playoffs, the Devils lost their opening round match-up to the Flyers. At the Awards Banquet at tthe end of the season, Scott won his first Norris Trophy as the league’s best defenceman.

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