New York Rangers' Mika Zibanejad  celebrates his goal with Sam...

New York Rangers' Mika Zibanejad  celebrates his goal with Sam Carrick during the first period against the Penguins in Pittsburgh on Saturday. Credit: AP/Gene J. Puskar

PITTSBURGH — Mike Sullivan returned to PPG Paints Arena on Saturday night for the first time since he and the Penguins parted ways last April, but the new Rangers coach had bigger problems than trying to keep a straight face when his tribute video was played on the scoreboard.

Sullivan was trying to figure out a way to beat his former team without having the services of Vincent Trocheck, who the Rangers said will be out on a week-to-week basis with an upper-body injury.

Special teams ended up being the key for the Blueshirts.

Adam Fox had two goals and an assist and the Rangers scored twice on the power play and once shorthanded to give them a 6-1 victory and a sweep of their two-game road trip that began Thursday in Buffalo.

“Special teams was good,’’ Fox said. “The PK [4-for-4 with a shorthanded goal] was great. The power play [2-for-4] wasn’t great, but you find a way — you put some pucks on net and get some goals. And, you know, I think sometimes that’s just how the power play goes. You put it to the net and get some. But we definitely cleaned up a lot five-on-five there in the second period.’’

Igor Shesterkin made 18 saves to earn his second win. Shesterkin has started the first three games and allowed only two goals, having saved 83 of 85 shots.

The Penguins, who had won their first two games against the Rangers on Tuesday at the Garden and against the Islanders on Thursday in Pittsburgh, largely outplayed the Rangers in the first period and outshot the visitors 9-4. However, the Rangers led 1-0 on Mika Zibanejad’s shorthanded goal at 7:40.

It came with Juuso Parssinen in the box for tripping and started when Fox cleared the puck out of the zone, springing Sam Carrick and Zibanejad on a two-on-one. Carrick carried the puck up the left side and feathered a pass between two defenders to Zibanejad, who redirected the puck in behind goalie Arturs Silovs, who had shut out the Rangers on Tuesday.

“I’m just reading to see what they give me at that point,’’ said Carrick, who had two assists. “If they take away the pass, then yeah, I’m looking to shoot. But I think as soon as I kind of looked to go for the shot, [the defenseman] kind of opened up. And the pass opened up.’’

Leading 1-0 after one period, the Rangers took control of the game in the second when they outshot the Penguins 14-3 and outscored them 3-1.

Pittsburgh tied the score at 3:04 on the first NHL goal of 18-year-old rookie Ben Kindel’s career, but Fox’s first goal put the Rangers ahead 2-1 at 6:06.

Will Cuylle scored the Rangers’ first power-play goal of the season at 9:25 — Conor Sheary’s shot/pass banked in off Cuylle’s skate — and Fox’s second goal, on the power play, made it 4-1 at 16:38.

The Rangers also won the third period, outshooting the Penguins 12-7 and outscoring them 2-0.

“I thought we got outplayed in the first 20 [minutes], and I thought Pittsburgh just played harder,’’ Sullivan said, “but I thought the response was terrific by [our] guys. I thought they played a much more determined game for the last 40 minutes. And I think that shows you what we’re capable of when we play with that focus and that determination.’’

With Trocheck out, Sullivan moved Zibanejad back to his natural center position and put him in Trocheck’s regular spot between wingers Artemi Panarin and Alexis Lafreniere.

The victory didn’t come without a cost, though. Defenseman Carson Soucy left early in the second period after he got tangled up with Pittsburgh’s Rickard Rakell and took an awkward, hard, headfirst fall into the boards. After the game, Sullivan said he was “being evaluated.’’

Early in the first period, the Penguins played a video welcoming Sullivan back and thanking him for his part in leading Pittsburgh to two Stanley Cup titles in his 10-plus years as coach.

“It’s emotional,’’ he said of seeing the video. “It means a lot. You know, I’m grateful for everything that we accomplished here during my time. I’m grateful for the opportunity to coach here in Pittsburgh for 10 years. I’m so grateful to the group of players over those years that performed the way they did that allowed us to have the success that we had. So when you watch a tribute like that, which I was very appreciative for . . .  it brings back a flood of emotions.’’

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