Guentzel and Kris Letang each had a goal and an assist as the Penguins won for the 12th time in 14 games. Sidney Crosby assisted Guentzel's winner, his 19th goal.
Rudolfs Balcers scored San Jose's only goal, and Adin Hill had 25 saves.
Domingue, Pittsburgh's third-string goalie, got the chance to make his debut after starter Tristan Jarry gave up six goals in Thursday's 6-2 loss to Los Angeles. Backup goalie Casey DeSmith is in COVID-19 protocols. Domingue appeared in just one game last season with Calgary.
"It was a long time coming," he said. "Ever since camp, I was prepared for this moment, I saw an opportunity and you either take it or you don't. I thought tonight I came in focused, and we played until the last whistle."
Balcers connected off a no-look, cross-ice pass from Erik Karlsson. All-Star Timo Meier was also credited with an assist. It was Balcer's first goal since Nov. 6 and his third of the season.
The Penguins tied it midway through the second period on Letang's breakaway. Letang sprinted for a loose puck outside the San Jose blue line and took it the rest of the way. He faked a forehand shot and then slipped a backhander past Hill for his third goal.
"We played a more committed game in the third period," Penguins coach Mike Sullivan said. "Our penalty kill was really good and got us going. ... The first two periods weren't nearly as good as what we feel we're capable of. Give San Jose credit, they played really hard, but we didn't play the type of game that we're capable of in the first 40 minutes."
San Jose had a great opportunity late in the second period when Guentzel was called for a four-minute double-minor for high sticking, but the Sharks were unable to capitalize.
"We had a lot of good chances," Sharks captain Logan Couture said. "We keep creating those chances and they're going to start going in soon."
The Sharks had two more power plays late in the third and failed to capitalize. They were 0 for 4.
The Sharks power play ranked 24th in the NHL going into Saturday, scoring on 17% of its chances.
"A power-play goal would've been nice," Sharks coach Bob Boughner said. "A lot of our guys are snake bit. We had guys in front of the net, but we're not putting them in. We had 41 shots, tried to make it hard on their goalie, just not a lot of puck luck."
Guentzel had an assist on Letang's goal to extend his road points streak to 16 games. Guentzel is among five players in NHL history with road points streaks of at least 15 games.
Pittsburgh activated F Brock McGinn from the COVID-19 protocol list. F Anthony Angello was reassigned to the taxi squad. ... Letang's goal moved him into a tie for sixth on the career franchise list with Hall of Famer Ron Francisco for points with 613. ... Sharks G James Reimer came off the injured list as a backup and could start Monday's game against Los Angeles, Boughner said. Reimer hasn't played since Jan. 4. ... D Jacob Middleton (concussion protocol) did not skate Saturday after skating the two previous days, Boughner said. ... Karlsson needs three more assists for his 500th.
Penguins: Wrap up a six-game road trip Monday night against Vegas.
Sharks: Conclude a four-game homestand Monday against Los Angeles.