Gourde scored for the fourth straight game when he put the Lightning ahead 2-1 at 12:44 of the second on a follow up of his initial shot.
"I just tried to get it on net and was fortunate enough that the puck came back right in front of me," Gourde said. "My stick was free, so I tried to shoot it right away."
Tampa Bay was credited with 15 blocked shots without defenseman Ryan McDonagh, who has a lower-body injury.
"In the end, that's how you win hockey games," Lightning coach Jon Cooper said. "It's not necessarily how many you put in the net, it's what you keep out. Aside from that one power-play going in early, we didn't give them much. Guys were committed to defending, and hence that's how you win 2-1 games."
The teams will play in Dallas again Thursday. The Stars are 0-3-1 in four games against the Lightning this season.
"To beat them, we know what to do; you just have to be willing to do it for the entire game," Dallas forward Andrew Cogliano said. "We have to do that Thursday night and if we do that, hopefully we'll get a win and build some momentum."
NOTES: Hintz fell awkwardly on his right leg early in the third and needed assistance to get from the bench to the locker room, but he was able to return. ... Lightning defenseman Andreas Borgman replaced McDonagh and had one blocked shot and one hit in 14:13 of ice time.