Ryan Suter got a phone call from Zach Parise, and his heart sunk with pity. Jason Zucker and most other teammates didn’t learn of Parise’s absence until they noticed his No. 11 jersey wasn’t hanging in his stall.

The moment it was announced that the Wild’s heart and soul would miss Tuesday’s game — a 4-3 overtime loss to San Jose — so he could be at his father’s side, heartbreak and emptiness filled Xcel Energy Center.

J.P. Parise, the popular former North Star and proud father of one of the Wild’s most affable, popular and hardest-working players, is at the end of a yearlong battle with lung cancer. J.P.’s den was converted into a hospice area last week, so son Zach knew there would be a point soon that he would need to put family in front of hockey.

“Life is so much bigger than hockey,” Suter said.

With all the pregame locker-room talk about their hurting teammate, the Wild played hard in Parise’s honor. But in the end, the skidding team lost again, this time relinquishing a two-goal lead and forcing overtime on a Zucker beauty before handing the extra point to the Sharks.

“Zach’s such a huge part of our team,” said Suter, who lost his own father before training camp. “For him to be going through what he’s going through is just awful. I couldn’t even imagine what he’s going through and what he has been going through.

“To play through it says a lot about who he is, and his dad would be proud of him.”

Zucker, who assumed Parise’s top-line left wing spot, scored two goals, assisted on another, had eight shots and was plus-3. Jason Pominville, who borrowed Parise’s “A” for a night, had two assists.

But with the Wild up 2-1 in the third, Joe Pavelski and Tommy Wingels scored 74 seconds apart to give San Jose a 3-2 lead. Charlie Coyle set up a driving Zucker for the tying score with 7:48 left in regulation, but for the fourth time in six home games, the Wild fell in overtime when Marc-Edouard Vlasic scored a 43-footer from the top of the left circle near the left boards.

It was the Wild’s 13th loss in 20 games and the latest bad goal surrendered by Darcy Kuemper. Coach Mike Yeo liked just about everything about the Wild’s game … except the goaltending.

“We’re not in a position where we can have anybody be below average, and it always starts and ends with goaltending,” Yeo said. “It’s a tricky one trying to be sensitive to his confidence, but that goal in overtime can’t go in.”

And that goal came after Kuemper kicked a weirdly bouncing shot by Wingels right back toward him, and he scored on the second chance for a 3-2 Sharks lead in the third. Kuemper is 24 and really in his first full season as the Wild’s No. 1 goalie, so Yeo knows his assessment is harsh. But he said, “That’s just the reality of the position, that’s what you sign up for when you play. … Guys need to elevate their games in every position.”

Kuemper, pulled in five starts since Nov. 13, ranks 53rd in the NHL with a .902 save percentage. Backup Niklas Backstrom ranks 60th (.896). It’s impossible for a team to win with the most important position letting in goals at that rate.

“I thought we competed hard. I thought we played well,” Suter said. “I’m sure the last couple Kuemps would like to have back.”

Asked how hard it is to play in front of erratic goaltending, Suter said, “It’s a team game. We’re going to stick together. He’s the future of this team, and we have to stand with him. He’ll get out of it. He’ll come around, and until he does we just have to play even harder.”

In the meantime, all other talk afterward surrounded Parise.

“Our guys banded together. Our guys wanted to play hard for him,” Yeo said.

Added Zucker, “He’s an emotional leader for us, and to see him going through what he’s going through is very tough. I can’t even imagine the pain he’s going through right now. As a team, we just want to make sure we’re here for him and show we truly care about him.”