A hyperactive Penguins defensive effort continued to slow down Pavelski, still the playoff leader with 13 goals, and make things difficult for Logan Couture, Joe Thornton and Brent Burns.
"Something we did in the first three rounds was to jump out early," Pavelski said. "We haven't quite got that yet. Moving forward, scoring first will play a big role in giving us a chance. There's no time for frustration. We have to keep going. The chances are there, we have to find a way."
San Jose has yet to lead at any point in the series other than after scoring in overtime in Game 3.
"We've been chasing the game the whole series by not scoring first," coach Peter DeBoer said. "That takes you out of your four-line rhythm. It affects all parts of your game. ... That's the biggest thing we have to fix. We have to find a way to get on the board earlier in the game instead of chasing it all night."
Pavelski did send five pucks at the net, one more than his total from the first three games combined.
"He's getting chances," Couture said. "The guy has 13 goals in the playoffs. That's pretty ridiculous. It's not easy to score goals. You have to keep believing they'll start going in."
The Sharks' power-play ranked third in the NHL during the regular season, and they have 18 man-advantage goals in the playoffs. The Penguins, fifth during the regular season in penalty kill percentage, have shown again and again that a good defense beats a good offense.
"There was tight checking and the refs were letting things go, but make no mistake, they are a good penalty kill team," Couture said. "We need to do a better job of creating shots. We have the extra man, we have to find the guy who's open."
The story for the Penguins after their 3-2 overtime loss in Game 3 was how to get forward Evgeni Malkin going after a slow start to the series. And how would the rookie goalie Matt Murray respond after giving up the soft goal to Ward and the winner to Joonas Donskoi.
Both passed with flying colors.
Malkin was energized from the start, helping setting up the first goal when he caught San Jose on a bad line change and sent Phil Kessel in on a rush. Jones stopped Kessel's shot, but Cole knocked in the rebound for his first career playoff goal.
Malkin then got his goal when he tapped in a perfect from Kessel for Pittsburgh's first power-play goal of the series.
"I didn't change my game a lot," Malkin said. "I wanted a little bit more to play with the puck."
Murray wasn't tested often early and went nearly the first half of the second period without facing a single shot.
"I'm just trying to have fun through all of this," Murray said. "It's been an absolute blast so far. I'm going to look to keep that same mindset going forward."
The Sharks made a strong late push, and he robbed Couture, left all alone in the slot after a turnover by Kris Letang, late in the second.
Murray then stopped Patrick Marleau on a breakaway and saved a one-timer by Joe Pavelski early in the third before allowing his first goal. Karlsson beat him on a rebound of Brenden Dillon's point shot with 11:53 to play.
But Murray didn't flinch and came up big again against Pavelski, keeping the NHL's leading goal scorer this postseason without a point in the final.