In his 19-year NHL career, Gelinas played in 1,273 games (62nd all-time at the start of this season) and scored 660 points. He played the 2002-03 and 2004-04 seasons with the Flames, and tied an NHL record by scoring three playoff series-clinching goals in the same year - including two in overtime - during the Flames' 2004 Stanley Cup run (and joining Ken Linseman in the record book in the process).
"The Eliminator," as Gelinas was known, is one just a handful of players to have reached the Stanley Cup Finals with four different teams; the left-winger won a Stanley Cup in 1990 as a member of the Edmonton Oilers and also played in the NHL Finals in 1994 and 2002. He also played two professional seasons in Switzerland (2004-05 and 2008-09).
A native of Shawinigan, Quebec, Gelinas made a splash in 1987-88 with the Hull Olympiques of the QMJHL with a 63-goal, 131-point campaign. He was named CHL Rookie of the Year and selected seventh overall by the Los Angeles Kings in the 1988 NHL Entry Draft. But Gelinas never suited up for the Kings. Two months after the draft, on August 9, 1988, he was included in the celebrated "Gretzky Trade" that sent Gelinas, Kings center Jimmy Carson, the team's first round picks in the 1989, 1991 and 1993 entry drafts, and a reported $15 million cash to Edmonton in exchange for Wayne Gretzky, Mike Krushelnyski and Marty McSorley.
Gelinas played six games for the Oilers in 1988 before being re-joining the Olympiques. In his first full NHL season in 1989-90, Gelinas had 25 points in 46 games, and won the Stanley Cup as Edmonton defeated the Boston Bruins in five games. Along with Joe Murphy and Adam Graves, he helped make up the popular Oilers' forward line known as "The Kid Line." Gelinas was the last player from the 1980s Oilers' dynasty active in the NHL.
He was traded to the Quebec Nordiques during the 1993 NHL Entry Draft and played 31 games for
Quebec before being claimed on waivers by the Vancouver Canucks. Gelinas was a major factor
in Vancouver's 1994 postseason run losing in seven games in the Stanley Cup Finals to the New
York Rangers. He and goaltender Kirk McLean were traded to the Carolina Hurricanes on January 3, 1998, where he spent five seasons before joining the Calgary Flames. He went on to play a year in Switzerland during the 2004-05 season before signing with the Florida Panthers for the 2005-06 and 2006-07 seasons. He concluded his NHL career in 2007-08 as a member of the Nashville Predators, where his season was cut short by a knee injury. He was Nashville's Masterton Trophy nominee that year.
Gelinas and his family have lived in Calgary since 2002. He and his wife, Jane, have three children - a son, Matthew, and daughters Cameron and Morgan. Matthew was selected by Swift Current in the 2010 Western Hockey League Bantam Draft.