Shea Theodore scored for the Golden Knights (31-25-14), who have lost three straight games and have scored one goal during that span. Akira Schmid made 16 saves.
Vegas remained one point behind the Edmonton Oilers for second place in the Pacific Division.
"Well, we scored one tonight, I guess that's a positive," Golden Knights coach Bruce Cassidy said. "I thought we had some decent chances in the first, a lot better than theirs. But we didn't finish. The power play didn't execute like it typically does (1-for-4). They broke us down on their (power play). They had some good east-west looks. I think that was the difference, if we could've been a little better on our power play."
Stamkos gave the Predators a 1-0 lead 40 seconds into the first period on a one-timer off of a clean face-off win by O'Reilly.
"It was one of those that [O'Reilly] said, 'How about I try to snap one back to you and you shoot it?' I said, 'Sure." And it worked," Stamkos said. "That's what happened. Those are a dime a dozen type of plays where it comes so clean and fast. I don't think anyone, including the goalie, reacted until it was in the net."
Vegas out-shot Nashville 20-4 in the first period.
"There was a lot to like about how we came out to play," Vegas forward Brett Howden said. "I think just the goals they got, we kind of gave them those chances. It's kind of on us, which is unfortunate. The only four real good chances they got, they scored. There's a lot to like about how we played tonight, but we've just got to do a better job of finding a way."
Stamkos made it 2-0 at 1:24 of the second period on a one-timer on the power play off a cross-ice pass from Filip Forsberg.
Tyson Jost scored short-handed to make it 3-0 at 11:56 of the second. Brady Skjei led a 3-on-1 rush after a turnover from Mitch Marner and he found Jost in the slot.
Theodore scored for Vegas to make it 3-1 at 13:10 on a wrist shot from the point that got through traffic and beat Annunen.
O'Reilly gave Nashville a 4-1 lead at 14:53 with a power-play goal, finishing off a cross-ice pass from Stamkos in the crease.
"As a group there's urgency there [on the power play]," O'Reilly said. "We're putting pucks at the net, and we're winning battles. We've got to keep building off of that. Obviously, the last couple of games that's helped us, and we've got to continue to do that."