Sullivan was then picked up off waivers in 1999 by the Chicago Blackhawks. Sullivan posted a new career high of 75 points in the 2001–02 NHL season.
Sullivan was traded to the Nashville Predators for a second-round pick in the 2005 NHL Entry Draft (Michael Blunden) and a second-round pick in the 2004 NHL Entry Draft (Ryan Garlock) on February 16, 2004.
Upon arriving in Nashville, put up 30 points in 24 games, including a hat trick in his first game with the Predators, and 10 points in his first 3 games with the team.
He was named the NHL's Offensive Player of the Week for September 9–16, 2005.
Sullivan sat out the entire 2007–08 NHL season because of a back injury.
Regular SeasonSeason Team Lge GP G A Pts PIM1995-96 New Jersey Devils NHL 16 5 4 9 8 1996-97 New Jersey/Toronto NHL 54 13 25 38 37 1997-98 Toronto Maple Leafs NHL 63 10 18 28 40 1998-99 Toronto Maple Leafs NHL 63 20 20 40 28 1999-00 Toronto/Chicago NHL 80 22 43 65 56 2000-01 Chicago Blackhawks NHL 81 34 41 75 54 2001-02 Chicago Blackhawks NHL 78 21 39 60 67 2002-03 Chicago Blackhawks NHL 82 26 35 61 42 2003-04 Chicago/Nashville NHL 80 24 49 73 48 2005-06 Nashville Predators NHL 69 31 37 68 50 2006-07 Nashville Predators NHL 57 22 38 60 20
NHL Totals 723 228 349 577 450