Gourde had a breakaway goal 4:25 into overtime and the Lightning rallied from a three-goal deficit to beat the Chicago Blackhawks 5-4 on Monday night.
Playing in his 13th game this season and 15th overall, Gourde beat Scott Darling after Victor Hedman set up the winner with his third assist of the game.
"A pretty good moment," Gourde said. "It was a pretty amazing feeling."
Tampa Bay, which trails Boston by a point for the second Eastern Conference wild card, got two goals from Jonathan Drouin. Ondrej Palat and Anton Stralman also scored, and Andrei Vasilevskiy, who got pulled 14 minutes into the first after allowing three goals on eight shots, returned to start the second and finished with 25 saves.
"It's not going to mean anything unless we get ourselves in (the playoffs)," Tampa Bay coach Jon Cooper said. "This was just another step, a really exciting one."
Artemi Panarin, Patrick Kane, Tomas Jurco and Richard Panik scored for the Western Conference-leading Blackhawks, who were coming off a 7-0 loss Saturday night at Florida. Darling stopped 25 shots.
"We had everything going our way there and then we started getting cute in the neutral zone," Blackhawks coach Joel Quenneville said. "We let them get back in the game."
After the Blackhawks went up 4-1 midway through the second on Panik's goal, Tampa Bay tied it at 4 on Drouin's goals and one by Stralman in a 4:39 span.
Chicago took a 3-1 lead after the first period on goals by Panarin, Kane and Jurco. Palat, playing in his 300th NHL game, had the Tampa Bay goal.
"We had such a good first period," Darling said. "A good start for the second and then they just turned it on. It was pretty impressive."
Palat and Drouin's second goal came on power plays after Chicago was penalized for delay of game after shooting the puck over the glass.
The Blackhawks have the 24th ranked short-handed unit in the NHL.
Nikita Kucherov had two assists to set a Tampa Bay record for points in a single month with 22. The right wing has four assists and 11 points during a five-game point streak.
NOTES: Chicago has won just five times in 19 regular season road games against the Lightning. The Blackhawks did win two of three at Tampa Bay in the 2015 Stanley Cup Final. ... Jurco stopped a 34-game goal drought, dating to Feb. 18, 2016. ... Palat has two goals and eight points in a five-game point streak. ... Lightning G Peter Budaj made three saves in the first.
Blackhawks: Complete a three-game trip Wednesday night at Pittsburgh.
Lightning: Play the second of four straight home games Thursday night against Detroit.