Filip Zadina and Givani Smith scored in regulation for Detroit, and Calvin Pickard - making his second start of the season - stopped 36 shots through overtime and all three Pittsburgh skaters in the tiebreaker.
''I'm not saying we outplayed them,'' Red Wings coach Jeff Blashill said. ''But I think we did a lot of things that you have to do in order to beat good teams and have a chance to win on the road.''
Jake Guentzel scored twice for the Penguins, who lost for the second time in two days following a six-game win streak. Pittsburgh is 17-2-2 in its last 21 games dating back to Dec. 4. Casey DeSmith had 30 saves for the Penguins, who have points in eight straight games overall (6-0-2) and 10 consecutive at home.
''I thought we played a better game,'' Penguins coach Mike Sullivan said. ''We knew this was going to be a tough game, playing back-to-back. It was a hard-fought point.''
In the shootout, Raymond beat DeSmith on the Red Wings' first shot, and Pickard denied Guentzel, Sidney Crosby and Kris Letang as Detroit snapped a three-game skid.
The Red Wings held the Penguins to just two goals 48 hours after an 8-5 loss at home to Chicago. Detroit had allowed 17 goals during its three-game losing streak.
Pickard has played 115 NHL games with five teams in eight seasons. He has 13 wins and a shutout during 27 appearances in the American Hockey League this season.
Pickard was recalled from the AHL on Wednesday and allowed three goals on 21 shots against Chicago before he was assigned to the taxi squad the following day.
''Calvin's a warrior,'' Blashill said. ''He battles to win games. We thought this was the right one for him.''
Guentzel tied the game 2-2 just 27 seconds into the third period. His forecheck behind the net forced a turnover along the boards. Crosby then sent a centering pass to Guentzel, who ripped a one-timer past Pickard to the blocker side for his 23rd of the season.
Smith opened the scoring for Detroit with 1:41 left in the first period. The Red Wings capitalized on a giveaway by Mike Matheson behind the net and Smith converted a rebound with a turning shot from the top of the crease for his third.
Guentzel tied it for Pittsburgh with a power-play goal at 5:54 of the second. Crosby sent a slap shot to the net and Guentzel put the rebound behind Pickard, giving the Penguins power-play goals in six of their last seven games.
The Red Wings regained the lead with a power-play goal of their own. Zadina scored his first goal since Nov. 30 with 3 1/2 minutes left in the middle period when he backhanded a rebound past DeSmith.
''Our guys want to win,'' said Blashill, who is one game from 500 as an NHL coach. ''It's a process at times to learn how to do that. They're working towards that.''
GUENTZEL NEARS 300 POINTS
Guentzel is one point from becoming the 26th player in team history to record 300 points in the NHL.
Guentzel, an All-Star this season, is also looking to become the seventh-fastest player in team history to reach 300 points.
Guentzel, who was selected No. 77 overall during the 2013 NHL Draft, is looking to become the seventh member of his draft class and first one selected outside the top-10 to reach 300 points.
Guentzel's first goal ended a three-game point drought. It was the longest he went without a point this season. Guentzel, who leads the team with 23 goals and 42 points in 38 games, only went consecutive games without a point once this season in October.
''I just think he's a terrific hockey player,'' Sullivan said. ''I think he's been one of the more consistent goal scorers in the league over the last couple years.''
MALKIN'S SEVEN-GAME STREAK
Evgeni Malkin continued a seven-game point streak with an assist on Guentzel's goal. He has four goals and seven assists in 10 games since making his season debut on Jan. 11.
Malkin has points in all five home games this season and points in 14 of his last 16 home games - five goals and 19 points - dating back to last season.
Malkin also has points in eight of his last nine games against Detroit. In 22 career games against the Red Wings, Malkin has 11 goals and 32 points.
Jakub Vrana and Troy Stecher practiced with the Red Wings on Thursday but have not rejoined the team. Thomas Greiss also returned to the team for the first time since entering the NHL's COVID-19 protocols on Jan. 17, but did not dress on Friday.
Vrana, who won a Stanley Cup in Washington, has not played this season after suffering a shoulder injury in training camp. Vrana, who skated in a non-contact jersey, was cleared to shoot the puck and is expected to return in late February. Stecher underwent wrist surgery on Nov. 4.
Sullivan considered forward Jason Zucker as week-to-week and ''probably longer term'' following core muscle surgery on Jan. 25.
Red Wings: Open a three-game homestand Saturday against Toronto.
Penguins: Continue a six-game homestand on Sunday against Los Angeles.
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