His Kings career was short lived, however, as he was part of the infamous deal that also sent Jimmy Carson, and the Kings's first round choices in 1989, 1991 and 1993 Entry Drafts and cash for Wayne Gretzky, Mike Krushelnyski and Marty McSorley on August 9 1988. He played six games for the Oilers in 1988, before being sent back to the Olympiques. In his first full season in 1989-90, Gelinas had 25 points in 46 games, and won his only Stanley Cup as a member of the Oilers, beating the Boston Bruins. Along with Joe Murphy and Adam Graves, he was made up a popular Oilers' forward line known as 'The Kid Line.' His Oilers career was a bit of a letdown, however, and his best season was a 40 point effort in 1990–91. Gelinas is currently the last active player from the 1980s Oilers dynasty remaining in the NHL.
He was traded to the Quebec Nordiques during the 1993 NHL Entry Draft for Scott Pearson, and he lasted only 31 games for Quebec before being claimed on waivers by the Vancouver Canucks. The move proved to be a good one for the Canucks, as Gelinas was a factor in the Canucks' 1994 postseason run. Though they lost in the Stanley Cup Finals to the New York Rangers in 7 games, Gelinas himself had an opportunity to force overtime late in the deciding game. With Ranger goaltender Mike Richter at his mercy, Gelinas wristed the puck into the post, coming within an inch or two of tying the game. He had a strong career in Vancouver during his four year tenure there. His best season came in 1996–97 when he scored 35 goals and 68 points, highlighted by a four-goal game, and being voted the team's Most Valuable Player after the season. However, a slow start the next season due to injury made him expendable to the Canucks, and the fan favorite was traded along with goaltender Kirk McLean to the Carolina Hurricanes on January 3, 1998. The move was part of a general 'house-cleaning' of fan favorites done by then-de facto general manager Mike Keenan, a pattern of his over the years with several NHL teams.
His Hurricanes career lasted four and a half seasons, and he was a role player who was primarily relied on for his penalty killing. His best season on the Hurricanes came in 2001–02 with 52 points, but his most memorable moment with the franchise came in the 2002 playoffs, when Gelinas scored the game-winning goal in Game 6 of the Eastern Conference Finals over the Toronto Maple Leafs, giving the Hurricanes their first-ever Stanley Cup Finals appearance. Their run ended after losing in five games to the Detroit Red Wings. He signed as a free agent with the Calgary Flames after the season ended.
Gelinas proved to be a bargain in his first season in Calgary. He notched 52 points and was one of the best players for the team that season. However, he would be the factor for another underdog team in 2004. The Flames entered that season missing the playoffs for seven straight seasons. They had a strong season that included efforts from longtime star Jarome Iginla and new goaltender Miikka Kiprusoff. The postseason proved that Gelinas could perform in the clutch, as he scored the series-clinching goal in each of the playoff series leading to the Stanley Cup Finals. Gelinas also came close to scoring a go-ahead goal in Game 6 of the Stanley Cup finals with the Flames leading 3–2 in the series, but the shot, which deflected off Gelinas' skate onto Lightning goaltender Nikolai Khabibulin's pad, went unreviewed and play was allowed to continue with no goal awarded.
Gelinas is almost unique in NHL history, having scored three playoff series-clinching goals in the same year (the only other player to do so was Ken Linseman), two of them in overtime. In fact, had his now dubbed "Phantom Goal" in the overtime of Game Six in the Finals not been disallowed by the referee, Gelinas would have scored all four series-clinching goals that year. Thanks to his clutch play, the Flames not only proved critics wrong by making the postseason and earning a Finals berth for the first time in 15 years, but also earning the unofficial moniker, "The Eliminator". Gelinas is one of the few players to have reached the Stanley Cup Finals with four different teams, having a major impact in every one of them.
On August 2, 2005, Gelinas agreed to a two-year, $1.9 million deal to play for the Florida Panthers. While Florida missed the playoffs in both years Gelinas was with them, he proved to be one of their consistent and dependable players, having played all 164 regular season games over the two seasons and scoring over 40 points in both seasons as well.
On July 26, 2007, Gelinas signed a one-year, $1.25 million deal with the Nashville Predators. The Predators made the playoffs that season, however Gelinas missed 25 games and the Predators' first round series in which they lost to the eventual Stanley Cup Champion Detroit Red Wings.
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Secretary of State John Kerry Delivers Remarks with Lithuanian Foreign Minister Linas Linkvicius Following Their Meeting
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