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. 

The 6-foot-4, 215-pound defenseman immediately flashed his skill when called up early in the 2013-14 season. Gelinas scored his first NHL goal 9:41 into his first game, a power-play goal against the Vancouver Canucks that began a 13-game stretch in which Gelinas scored two goals and seven points as the Devils went 8-3-2.

On Jan. 21, 2014, Gelinas had a goal and two assists in a 7-1 win against the St. Louis Blues, making him the Devils' first rookie defenseman to score three points in a game since Brian Rafalski on Feb. 13, 2000. He also accomplished something his baseball-playing family members never did by playing at Yankee Stadium on Jan. 26, 2014 against the New York Rangers as part of the NHL's Stadium Series.

The Vanier, Ontario, native finished his rookie season with 29 points, including 17 power-play points, which tied him for second on the Devils with Patrik Elias and Jaromir Jagr. 

On Feb. 29, 2016, the Devils traded Gelinas to the Colorado Avalanche for a third-round draft pick.