Sylvain Cote came up through minor hockey in Quebec City and played midget hockey with the Ste-Foy Gouverneurs of the Quebec AAA league. In 1982-83, he joined the QMJHL's Quebec Remparts and scored 34 points as a major junior rookie. The following season, he improved to 65 points on the blueline and was named a Second Team All-Star. That summer, the Hartford Whalers selected him 11th overall in the 1984 NHL Entry Draft. After a year at the NHL level, Cote returned to the junior ranks in 1985-86 and scored 43 points in 26 games with the QMJHL's Hull Olympiques and was named a First Team All-Star. In the QMJHL playoffs, he scored 34 points including a league-best 28 assists in just 13 games. Cote also won a silver medal with Canada at the 1986 World Junior Championships and was named a tournament All-Star.
Cote played five years in Hartford before being traded to the Washington Capitals on September 8, 1991. In 1993-94, Cote registered a career-high 51 points and remained a steady performer on the Capitals' defense until being traded to the Toronto Maple Leafs for Jeff Brown in March, 1998. During the 1998-99 season, Cote was instrumental in helping the Leafs improve 28 points to reach the post season for the first time in three years.
In the fall of 1999, Cote was traded to the Chicago Blackhawks for a 2nd-round draft and midway through the season was traded with Dave Manson to the Dallas Stars. During the season Cote reached a personal milestone appearing in his 1000th career game and during the playoffs, helped the Stars reach the Stanley Cup finals where they lost to the New Jersey Devils.
In the summer of 2000, Cote signed as a free agent with the Washington Capitals and went on to play two full seasons with the club before calling it a career after being released after only one game in 2002-03.