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. On 9 March 2006, it was announced that Svatoš sustained a fracture to his right shoulder that forced him to miss the rest of the 2005–06 season. At the time of his injury, Svatoš led the NHL in game-winning goals with nine, which tied an NHL record for game-winning goals by a rookie. He was also one of the top rookie scorers with 32 goals in 61 games. Svatoš' numbers dropped in 2006–07, his second season, as he recorded 15 goals and 15 assists in 66 games while suffering a recurring groin injury throughout the season. Svatoš was leading the Avalanche with 26 goals during the 2007–08 campaign when he suffered a torn ACL in a game against the Los Angeles Kings on 1 March 2008. Svatoš missed the final sixteen games of the season and the additional playoff series, but still placed second in goals on the team. On 25 July 2008, Svatoš re-signed with the Avalanche for a further two years, avoiding arbitration scheduled on the same day. He managed to return to the opening night roster for the 2008–09 season, recovering from his ACL tear gradually as the season went on. He played in 69 games with the Avalanche before injuring his hand on 7 April 2009, in a 0–1 overtime loss against the San Jose Sharks in San Jose, ending his play with three games left in the season. His 14 goals tied Wojtek Wolski for fourth on the Western Conference last-placed Avalanche. In the 2009–10 season, Svatoš was limited to 54 games, again missing 18 games through groin and chest injuries. With a sixth consecutive NHL season affected from injury, he suffered from a loss of form and under new coach Joe Sacco, was relegated to a reserve role and recorded a career low 7 goals and 11 points. Without a contract offer, Svatoš left the NHL and signed a one-year contract during the early stages of the 2010–11 European season with Russian team, Avangard Omsk of the KHL, on 24 September 2010. In 19 games with Omsk, he posted 3 goals and 8 points before he was granted a release, after both sides agreed to terminate the deal on 23 December 2010. On 28 December 2010, Svatoš returned to North America with NHL ambitions and signed a one-year, two-way contract with the St. Louis Blues. However, in order to return to the NHL he was placed on waivers due to starting the season in Europe and the following day on 29 December, was subsequently claimed by the Nashville Predators. On 31 December 2010, he dressed for the Predators to make his 2010–11 season debut in an away game win over the Minnesota Wild. In his fourth game, Svatos registered his only goal for the Predators in a 5–2 victory over the Los Angeles Kings on 6 January 2011. Leading up to the trade deadline, Svatos was waived by the Predators after nine games and was subsequently claimed by the Ottawa Senators on 24 February 2011. Svatos earned a regular shift with the Senators and on 27 March 2011, he scored his second goal of the game, which marked his 100th career NHL goal, in a defeat by the Atlanta Thrashers. Svatos appeared in 19 games for the Senators before he suffered a season ending concussion as a result of an check from Jay Rosehill in a late season contest against the Toronto Maple Leafs. After sitting out the entire 2011–12 season recovering from injury, Svatoš in a bid to return to the NHL, signed a try-out contract to attend training camp of the Florida Panthers for the 2012–13 season following a resolution to the NHL lockout on 7 January 2013. Upon completion of the abbreviated training camp, Svatoš was released two days prior to the regular season on 17 January 2013. Shortly after leaving Panthers camp, Svatoš agreed to sign for KHL team Slovan Bratislava from his home country for the remainder of the 2012–13 season on 22 January 2013. Svatoš opted to remain in Slovakia the following season. Transferring as a free agent to sign a one-year contract with Košice of the Slovak Extraliga on 18 September 2013, he has helped his hometown club to win their seventh league title in the final season of his hockey career.
