Jurco began playing hockey for HC Kosice in his native Slovakia before moving to North America to play for Saint John of the Quebec Major Junior Hockey League during the 2009-10 season. He made the league finals in each of his three seasons with Saint John, winning the Memorial Cup championship in 2011. Jurco was then selected by the Detroit Red Wings in the second round (No. 35) of the 2011 NHL Draft.
After signing a three-year, entry-level contract with the Red Wings, Jurco was assigned to the American Hockey League for 2012-13 and helped Grand Rapids win the Calder Cup. He made his NHL debut on Dec. 15, 2013, at home against the Tampa Bay Lightning, and scored his first NHL goal against the Anaheim Ducks two nights later in Detroit.