Handzuš played for hometown club, HC ’05 Banská Bystrica of the Slovak Extraliga before joining the National Hockey League (NHL) in 1998.

Handzuš played for the St. Louis Blues, Phoenix Coyotes, Philadelphia Flyers, Los Angeles Kings, San Jose Sharks and the Chicago Blackhawks, with whom he won the Stanley Cup with in 2013.

[4] Handzuš was traded on 13 March 2001, along with Ladislav Nagy, Jeff Taffe and two first-round draft picks, to the Phoenix Coyotes in exchange for Keith Tkachuk.

[citation needed] On 12 June 2002, Handzuš was traded along with Robert Esche to the Philadelphia Flyers in exchange for Brian Boucher and a third-round draft pick.

[citation needed] On 28 May 2014, with the Blackhawks facing elimination in Game 5 of the Western Conference Finals, Handzuš scored a game-winning goal in double-overtime against Los Angeles Kings, the eventual Stanley Cup champions.