Svatoš was drafted 227th overall by the Colorado Avalanche in the 2001 NHL Entry Draft. He played his first NHL games for the Avalanche in the 2003–04 season. Following a strong performance in the Avalanche's second round loss in the playoffs, he returned to the Avalanche's AHL affiliate, the Hershey Bears, during the 2004 NHL Lockout. Svatoš recorded his first career hat trick in the NHL against the Calgary Flames in a 7–3 win on 10 October 2005. He was chosen to play in the 2006 Winter Olympics in Turin, Italy, as part of the Slovak national team.