Phil Kessel scored and Matt Murray made 22 saves for Pittsburgh (43-26-11), which would have secured a spot in the postseason with a win.
"We can't be frustrated, it's a useless emotion at this point," Penguins coach Mike Sullivan said. "We've just got to make sure we get ready for the next one. That's the mindset that we have to have. We still have to solidify a playoff spot."
WATCH: [All Penguins vs. Red Wings highlights]
Tyler Bertuzzi had two goals and an assist and became the first player in Red Wings history to have three or more points in four straight games.
"I think I'm a little shocked right now; it is hard to comprehend this," Bertuzzi said. "I just have to thank my teammates, and especially my linemates. We've having fun playing hockey right now."
Detroit coach Jeff Blashill was stunned that the 24-year-old forward had done something unprecedented for a team with a 93-year history.
"You think of the players for this franchise and the winning that's been done here and the number of goals that have been scored in different eras … I couldn't believe it," Blashill said.
Jimmy Howard made 38 saves for the Red Wings, (32-38-10) who have won six in a row, their longest streak since a six-game stretch from Oct. 17-27, 2016.
Detroit's top line of Bertuzzi, Dylan Larkin and Anthony Mantha have combined for 17 goals and 38 points in the six-game winning streak, including all four against Pittsburgh.