Mackenzie Blackwood made 22 saves for the Sharks (15-35-5), who have lost four of five and were shut out or the ninth time this season.
"I know it was a 4-0 loss, but I thought we were working really hard," Sharks forward Kevin Labanc said. "We just didn't get the right bounces, and that was a good goalie we were shooting on this afternoon. You just put your head down and stick with it and don't let this loss rub you the wrong way, because I think you can take a lot of good from this game as well."
Michael Amadio gave Vegas a 1-0 lead at 2:28 of the first period on a breakaway.
"It's just inexcusable. It can't happen," Sharks coach David Quinn said. "We started out great. We're ready to play. First two-and-a-half minutes we were buzzing. Crossbars. Chances. Then we gave up, like, our 38th breakaway in three games."
William Karlsson made it 2-0 at 4:25, scoring on the rebound of a shot by Martinez.
Morelli extended the lead to 3-0 at 19:12, deflecting in a cross-ice pass from Alex Pietrangelo on the power play.
"I didn't see it go in right away," Morelli said. "Once I knew it was in, it was pretty cool. We were hooting and hollering a little bit. It's a special moment for sure. I got to see the replay with my family (celebrating), too. It's hard to put into words, but it was pretty special."