SAN JOSE — I’m beginning to believe that the Sharks and the Vancouver Canucks are not Facebook friends. And that they sincerely loathe each other.

I’m also thinking it may not matter much longer. At least in this playoff series.

I came to both of these realizations at the very same moment Sunday night: During a faceoff in the third period, when the Canucks’ normally congenial Henrik Sedin rose up and punched the Sharks’ Logan Couture in the jaw.

“He didn’t even go for the puck on that one,” Couture said, still sounding a bit surprised. “He just went for me.”

After Sedin went in the penalty box, Couture subsequently expressed his own antipathy 21 seconds later by scoring his second power-play goal of the period. This gave the Sharks a 5-1 lead on the way to a 5-2 victory that puts the Sharks ahead 3-0 in the best-of-seven series.

“We don’t like them,” Couture said afterward of the Canucks. “Don’t like the way they play.”

On Tuesday night, if he and the Sharks take care of business, Vancouver will play no more in the spring of 2013. And after what the HP Pavilion witnesses saw Sunday night, there’s no reason to believe the Sharks can’t sweep an opponent for the first time in franchise history.

Although Sunday’s game was close for two periods, the Sharks never trailed, and the Canucks never seemed in true danger of taking a lead or taking control. For three entire games, the Sharks defense has shown how to keep Vancouver’s attack mostly away from the net and mostly off the scoreboard. Antti Niemi has never looked better in goal. Offensively, the goals are coming from the right people — Couture, Patrick Marleau, Joe Pavelski. Plus, full credit to our beloved Los Tiburones for scoring cinco goals as a salute to Cinco de Mayo. Away from the scoreboard, the Canucks’ body language (and that Henrik Sedin punch, along with Vancouver’s five chippy penalties after that one) tells you that they are discouraged and bumfoozled.

So you’d have to say, given all the evidence, that the series is decided. But that does not mean it is over.

Two years ago, the Sharks took a 3-games-to-0 advantage over the Detroit Red Wings and then lost three in a row before pulling out a thrilling but exhausting Game 7 victory.

Which is why Sharks coach Todd McLellan said this at his postgame presser: “Tomorrow I will remind them that the last time we were in this situation, we had to play seven.”

According to Pavelski, that won’t be necessary.

“Everybody knows,” Pavelski said. “Everybody knows. We’ve been in that situation before. We know what to expect.”

The guys who were in Sharks uniforms in 2011 definitely know and remember. The newer players might still need to be reminded. So what does Pavelski recall about what went wrong to allow Detroit back into the series?

“I’m not even worried about it,” Pavelski said. “That’s been a while ago.”

So he’s wiped out the painful memory?

“I’m getting old,” Pavelski said, tongue planted firmly in cheek. “I’ve got a kid now.”

It’s important for the Sharks to finish off Vancouver for the same reason it’s important for any team to finish off any other team quickly in the playoffs: There’s more time to recover physically and prepare for the next round. For example, after the Detroit series went seven games in 2011, the drained Sharks ended up losing the Western Conference finals to a fresher team from … that’s right, Vancouver.

“This is a different team,” Couture said of the current Sharks.

Tuesday is the perfect time to prove that.

Contact Mark Purdy at mpurdy@mercurynews.com. Follow him on Twitter at twitter.com/MercPurdy.