Baseball may have run in Gelinas' family, but hockey was in his blood. His father, Marc Paul, was a minor-league pitcher and his brother, Karl, was drafted by the then-Anaheim Angels, but Gelinas focused his talents on the ice.
Gelinas was selected by the New Jersey Devils in the second round (No. 54) of the 2009 NHL Draft and spent time with Lewiston, Chicoutimi and Saint John of the Quebec Major Junior Hockey League. Following two seasons with Albany of the American Hockey League, he made his NHL debut with the Devils in the next-to-last game of the 2012-13 season.