Bryan Rust knows there are plenty of questions about the Pittsburgh Penguins at the moment.

And the right winger acknowledges the solutions aren’t plainly obvious.

“If we would have had all the answers, we wouldn’t have done the things that have happened this past however long,” Rust said Tuesday in Cranberry. “Obviously, we’re trying to search for answers and search for ways to be more consistent.

“That’s our goal right now: to get to that as fast as we can.”

That search remained unfulfilled Wednesday as the Penguins were defeated by the Detroit Red Wings, 3-2, in overtime at PPG Paints Arena. It was their fourth loss in their past five games (1-2-2).

A goal by Red Wings defenseman Simon Edvinsson — his second of the season — at 1 minute, 30 seconds of overtime was the difference.

The result came approximately 48 hours after a seismically embarrassing 7-1 home loss to the Dallas Stars and a little more than 24 hours after sturdy third-line center Lars Eller was traded to the Washington Capitals for a couple of mid-round draft picks.

These are bleak times for the Penguins. But Wednesday’s loss offered a few molecules of hope by simply not being as repugnant as Monday’s bludgeoning.

“Obviously, a loss is a loss,” Rust said following Wednesday’s game. “But I think the way we responded — we went down two — was a (heck) of a lot better than the way we responded the other night. Obviously, Rome wasn’t built in a day. We’re trying to get this thing going in the right direction as fast we can. That was a good step.”

What wasn’t good was the loss of forward Blake Lizotte, who opened the contest as the third-line center as Eller’s immediate replacement.

That assignment came to an end when he left the contest at 16:24 of the first period after being struck in the face by a puck.

Coach Mike Sullivan did not provide a substantive update on Lizotte and simply said he was still being evaluated for an undisclosed injury. He missed the first 11 games of the regular season after taking a puck to the face during a preseason contest, resulting in a concussion.

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Following a scoreless first period, the Red Wings struck when forward Jonatan Berggren scored his first goal of the season exactly one minute into the second frame.

Stealing a puck inside his own blue line, Red Wings defenseman Jeff Petry backhanded a pass off the right wing boards of the neutral zone, allowing Red Wings forward Vladimir Tarasenko to gain the Penguins’ zone on the right wing.

Allowing the play to develop, Tarasenko dished a cross-ice pass to the opposite wing for Berggren, who pumped a wrister from near the left dot past goaltender Alex Nedeljkovic’s blocker on the near side. Tarasenko and Petry had assists.

Red Wings forward Patrick Kane claimed his third goal during a power-play sequence at 5:15 of the second period.

After Penguins forward Anthony Beauvillier and defenseman Ryan Shea were unable to claim a bouncing puck off their own left wing wall, Red Wings forward Dylan Larkin gloved it down and slid a pass from the lower left circle through the skates of Penguins defenseman Ryan Graves.

Situated alone in the right circle, Kane accepted the feed and ripped a one-timer over Nedeljkovic’s glove on the near side. Larkin and forward Lucas Raymond registered assists.

A determined effort by Rust led to his fourth goal 124 seconds later.

After stealing an errant pass by Kane, Penguins forward Michael Bunting initiated transition out of his own zone and generated a two-on-two rush with Rust. Crossing over at the red line, Bunting left a drop pass for Rust, who rushed into Detroit’s zone on the left wing. Surging past a passive stick check by Red Wings defenseman Moritz Seider, Rust cut across the front of the crease and avoided a poke check by goaltender Cam Talbot before tucking a forehand shot by his left skate. The lone assist belonged to Bunting.

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Rust has a habit of generating offense with that type of maneuver.

“I’ve seen that goal I don’t know how many times now,” Nedeljkovic said. “He’s got a knack for it, beating guys wide like that and finding the far post. That was huge. Got us going, obviously, and same thing, we responded with two quick ones of our own. We played on top of them from there, it felt like.”

Beauvillier’s fifth goal of the season — and second in as many games — tied the score 2-2 at 12:23 of the second.

Gaining the offensive zone on the right wing, Penguins forward Sidney Crosby pulled up at the point and fed a cross-ice pass to defenseman Marcus Pettersson gliding up the left wing. Going deep below the near circle, Pettersson fended off Red Wings forward Christian Fischer and slipped a clever forehand pass through a handful of bodies to the opposite side of the crease, where Beauvillier buried an easy forehand shot. Pettersson and Crosby claimed assists.

Beauvillier is tied with forward Evgeni Malkin for the second-most goals on the team.

“(Beauvillier) has scored some goals for us so far,” Sullivan said. “I hope he can continue to help us there because certainly, we’re going to need it. Those are the reasons we’ve tried him with Sid or the top-six (forwards). Regardless of where we play him in the lineup, he’s going to bring that element.”

After a scoreless third period — in which the Penguins controlled shots, 11-7 — the Red Wings claimed victory in the extra frame.

Going deep into the right corner of the offensive zone, Red Wings forward Alex DeBrincat dished a pass to the top of the left circle. Accepting the puck, Edvinsson faked a shot, causing Rust to slip to the ice. With the opening created by that ruse, Edvidsson released a wrister that roasted Nedeljkovic’s glove. DeBrincat and Kane had assists.

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Nedeljkovic stopped 28 of 31 shots as his record slipped to 2-3-3.

Despite the result, the Penguins found optimism — even if just incrementally — over the improvement from Monday’s loss.

“All four lines play better tonight, for sure,” Malkin said. “It’s a great night for our team, I think, because it was a small step (toward) a better game. It’s hard to explain, but again, I hope next game we play the same, and we have a better chance to win. Little bit better and some luck, we win next game, for sure.”

Notes:

• Penguins rookie forward Sam Poulin made his season debut. Opening the contest on the third line, he logged 10:04 of ice time on 14 shifts, including 57 seconds on the penalty kill. He also recorded one penalty for two minutes and one shot on three attempts.

• Tristan Jarry served as Nedeljkovic’s backup. It was the first NHL contest Jarry dressed for since Oct. 18.

• With the 35-year-old Eller being traded, the average age of the Penguins’ roster dropped from 30.2 to 29.7.

• Pettersson (131 points) surpassed forward Al McDonough (130) for 72nd place on the franchise’s career scoring list.

• In 37 career games against the Red Wings, Crosby has 47 points (18 goals, 29 assists).

• In 13 career games against the Red Wings, Bunting has 15 points (six goals, nine assists).

• Penguins rookie goaltender Joel Blomqvist and defenseman Jack St. Ivany were healthy scratches.

• The Penguins’ last overtime loss to the Red Wings was a 5-4 setback at PPG Paints Arena on Dec. 28, 2022. The Penguins yielded a four-goal lead in that contest before losing via a goal by defenseman Jake Walman.

• In 26 career games against the Penguins, Kane has 31 points (eight goals, 23 assists)

• In 15 career games against the Penguins, DeBrincat has 17 points (seven goals, 10 assists).

• In 11 career games against the Penguins, Raymond has 13 points (five goals, eight assists).