Gourde made it 2-1 with a breakaway goal at 13:01 of the second period. He has scored in the past two games after 35 straight without a goal.
"That's how it goes right," Lightning coach Jon Cooper said. "You don't score for a while and all of a sudden they start coming for you. Probably when you get that first one it's a monkey off your back or whatever the term is."
Edmonton had the two power plays in the game and managed one shot on goal.
"Usually our power play, in the past month or two, seems like it's been able to get us a goal at a big time in the game," Oilers forward Alex Chiasson said. "We probably weren't as sharp as we're used to tonight."
Cedric Paquette made it 3-1 with an empty-net goal with 56 seconds remaining in the third period. Brayden Point had an assist to extend his point streak to nine games (13 points; two goals, 11 assists).
"They were a fast team, we battled hard, we had a lot of looks, we only gave up two," Jones said. "If we put a couple of those in the back of the net, it's a completely different game."