He turned pro immediately after completing his final campaign with the Frontenacs. He was no instant splash with the Habs, however. Instead, he had to bide his time with frequent stints with the AHL's Fredericton Canadiens.

It wasn't until 1997-98 that Rivet finally caught on as a Habs' regular. He did so by establishing himself as a true team player, concerned only with his club's success. He has also pleased the coaching staff with his stay-at-home, rock-solid defensive play in his own zone accentuated by a rather useful mean streak. After a career high 17 points in 1999-00, Rivet battled injuries the following year and was limited to just 26 games before bettering his offensive totals in 2001-02 and improving on his season high from the 1999-00 season with 25 points.

Rivet entered his ninth season with the Habs in 2002-03 and continued to be one of the team's on-ice leaders. Although the team failed to qualify for the post-season, Rivet's performance throughout the season earned him an invite to the 2003 World Championships.

In 2006-07, after setting a new career high in points with 34 in the 2005-06 season, Rivet was traded to the San Jose Sharks one day prior to the NHL trading deadline. After ending the season with the Sharks, Rivet spent a full season in San Jose where he tallied 35 points in 74 regular season games, setting new career highs. He appeared in 13 playoff games before the Sharks dealt the blueliner to the Buffalo Sabers.

Rivet's tenacious play and veteran presence made him a natural leader in Buffalo. On October 8, 2008 he was named captain of the Sabres, making him the 23rd player to wear the "C" for the Sabres.

On February 24, 2011, the Sabres waived their captain and Rivet was subsequently picked up off waivers by the Columbus Blue Jackets.