Neal was the final shooter after Dan Cleary broke his stick on a wrister on Detroit’s third shot. Neal skated in and buried a wrister into the right corner to give Pittsburgh the two points.
Pascal Dupuis had two goals and an assist while Chris Kunitz added a goal and an assist for the Penguins, who won for the third time in the past four games.
Brent Johnson made 37 stops as Pittsburgh moved to four points back of Philadelphia for first place in the Atlantic Division and the top spot in the Eastern Conference. Pittsburgh has nine games to play while Philadelphia has 11.
Prior to the game, Pittsburgh learned that forward Matt Cooke will miss the rest of the season and the first round of the playoffs due to a flagrant elbow he threw to the head of New York Rangers defenseman Ryan McDonagh in Sunday’s game.
Cleary and Valtteri Filppula each posted a goal and an assist for the Red Wings, who have dropped their past two. Jimmy Howard gave up four goals on 15 shots before being pulled in the second period. Joey McDonald finished the game in net and stopped 10 shots.
Detroit has 95 points on the season and holds a nine-point lead over Chicago for first place in the Central Division. Also, Detroit is in second place in the Western Conference and is eight points back of Vancouver. The two will meet in Detroit on Wednesday.
Pittsburgh made it a 4-0 game and chased Howard from the net when Tyler Kenndey lifted a backhander in off a rebound with 6:44 to play in the second.
However, Detroit got one back with 2:19 to play in the second as Henrik Zetterberg threw a backhander on net from the left circle that hit off the skate of Kris Letang and went in.
Just 1:57 into the third it was a 4-2 game as Filppula fought off a defender down low at the left side and got it into the net.
Skating on the power play, Detroit made it a 4-3 game as a left circle faceoff win saw Niklas Kronwall blast a shot on net from the right point that Cleary tipped in at the 8:06 mark.
Detroit then tied the came 2 1/2 minutes later with another power-play marker as a pass by Filppula from the left to the right saw Modano use a high wrister to get the puck over the glove of Johnson.
From there the score remained tied through the rest of regulation and overtime to force the shootout.
Pittsburgh got a goal from Dupuis with 4:46 left in the first and it was a 2-0 game with 42.4 seconds left in the opening frame as Kunitz followed up a rebound to stuff the puck past Howard.
Pittsburgh took a 3-0 lead with 9:09 to play in the second while shorthanded as Dupuis lost the puck while making a move, but was able to grab it behind the net and stuff it in from the right side for his 13th goal of the season.
Pittsburgh plays in Philadelphia on Thursday…Pittsburgh won both meetings this season…Detroit went 2-for-4 on the power play while Pittsburgh was 0- for-3…Detroit forwards Pavel Datsyuk (lower body), Johan Franzen (undisclosed) and Jiri Hudler (illness) all missed the game.