Gourde gave Tampa Bay a 2-1 lead at 6:22 of the third when he took a stretch pass from Victor Hedman and beat Reimer with a snap shot off the left post from the top of the right circle.
Barclay Goodrow scored into an empty net at 18:44 for the 3-1 final.
"We see these guys a lot, they know us, we know them, and it feels like a playoff game out there," Gourde said. "Obviously, we needed a better game tonight, but we were fortunate enough to come up with the win because McElhinney was amazing in the net."
McElhinney, who was playing his third game this season and allowed six goals on Feb. 15 (a 6-4 loss to the Florida Panthers), came up with several big saves for the Lightning, including a pad save on a one-timer from below the left hash marks by Brady Skjei with 2:49 remaining.
"I don't know if we gave out three stars," Tampa Bay coach Jon Cooper said. "But he should've been star one, two and three."