PITTSBURGH — The Penguins were in complete control Thursday — of both this game and their playoff standing — when they took a 5-3 lead on Jeff Carter’s short-handed goal.

PPG Paints Arena was rocking and the Detroit Red Wings reeling. It looked like the Penguins were well on their way to a huge win. But then they did it again.

The Red Wings scored with 7:04 left in the third period then tacked on another about two minutes later. The second one gave Lucas Raymond the hat trick.

Somehow, the Penguins recovered to win, 6-5, in overtime. Erik Karlsson ripped one past Red Wings goalie Alex Lyon with 3:20 remaining in the extra session.

Bryan Rust was a monster in the win, scoring once and dishing out two assists.

Thursday’s matchup was close to an elimination game for both teams, who both entered Thursday night in a tie for ninth in the conference, with 84 points each.

The teams traded tallies in the opening period, with two scored in the first four minutes. Kris Letang played a prominent role in three goals — two for Detroit.

Drew O’Connor got the Penguins on the board just 2:40 into the game. Sidney Crosby made everything happen. He banked the puck off the back of Detroit’s net to shake his captain counterpart, Dylan Larkin, then got it to Rust. He could not beat Lyon, but O’Connor was at the crease to nudge in the loose puck.

The Red Wings answered back just 59 seconds later with Raymond’s first goal. Alex DeBrincat picked Letang’s pocket and immediately fired the puck on the net. Raymond buried the rebound after Alex Nedeljkovic stopped the initial shot.

Letang scored off the rush to put the Penguins back in front. But during the final minute of the period, his errant pass led to a sudden 3-on-2 for the Red Wings. Raymond tucked in his second of the game with 14 seconds left on the clock.

In a game of such magnitude, that was an unfathomable lapse by the Penguins.

It turns out there was more to come in what was their most important game yet.

The two sides trading chances and rattled posts until Crosby gave the Penguins a 3-2 lead eight minutes into the second period. Rust had another spectacular setup, zipping the puck through three Red Wings to Crosby at the back post.

By that point, the game already had a real playoff feel. Things got even chipper from there on out. Crosby and Letang both had heated moments with opponents.

Rust made it 4-2 later in the second period, pulling in a pass from Reilly Smith, whipping one in off the crossbar and celebrating like he knew he was scoring.

Pittsburgh allowed another late goal in a period. Jeff Petry got it for Detroit. And after Carter’s short-handed goal put them back up two, the Penguins collapsed.

The defense pair of Marcus Pettersson and Karlsson were on for both of those goals. Karlsson left the slot vacant on Larkin’s goal. Pettersson then lost a race for the puck, letting Raymond to skate in on a breakaway and tie the score.

It was the fourth time in the last 10 games they lost a two-goal lead in the third.

But Karlsson redeemed himself in overtime, giving the Penguins a rare 3-on-3 win.

ICE CHIPS

— Lars Eller was in the lineup Thursday after missing Wednesday’s practice due to illness. The only change was Radim Zohorna stepping in for Jesse Puljujarvi on the fourth line. It was the towering forward’s first NHL game since Jan. 15.

— John Ludvig and Vinnie Hinostroza were Pittsburgh’s scratches. The Penguins called Hinostroza back up from the American Hockey League before the game.

— Michael Bunting now has 14 points in 18 games with Pittsburgh. He earned a primary assist when he made a nice, subtle pass to spring Letang for his goal.

— The Penguins placed defenseman Ryan Graves on long-term injured reserve, which will keep him out through the end of the regular season. Graves, who has sat out seven games with a concussion, skated on an individual basis Thursday.

— Penguins players selected Crosby as their team MVP for the fourth season in a row. He also won the Players’ Player Award for the sixth time in his career.

STAT N’AT

1,591 — With his assist in overtime, Crosby moved out of a tie with Phil Esposito into 10th all time on the NHL’s scoring list. The captain his 1,591 career points.

COMING UP

The Penguins are scheduled to practice Friday ahead of their next game, a Saturday showdown against the Boston Bruins at PPG Paints Arena.

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