The Golden Knights, who were 4-for-10 on the power play in the past four games, went 0-for-3 against the Sharks' League-leading penalty-killing unit (90.2 percent).
"We were a little too much on the outside there," Golden Knights forward Paul Stastny said. "When you're scoring sometimes and you get comfortable, you try to get cute. When we're successful on the power play, we're playing downhill. We get the puck, attack with it, put shots on net. They did a good job taking the lanes away, and that's what we're trying to find."
Meier scored with a backhand at 1:26 of the second period to give the Sharks a 1-0 lead.
McNabb tied it 1-1 at 9:42 of the third period on a wrist shot from outside the left circle. It was his first goal in 22 games.
The Golden Knights outshot the Sharks 28-17 through two periods but were outshot 12-10 in the third period and overtime.
"We wanted to be better," Couture said. "We didn't have a good effort [against the Edmonton Oilers on Tuesday, a 5-2 loss]. We weren't hard enough. We weren't ourselves. Tonight we played a little bit more like our game."