Neal's forehand wrist shot high to the glove side of Detroit's Joey McDonald enabled the Pens to secure the win after allowing the Red Wings to rally from a 4-0 second-period deficit.
Pascal Dupuis netted a pair of goals and added an assist while Chris Kunitz contributed a goal and a helper for the Penguins, who won for the third time in four games and moved to within four points of Philadelphia atop the Eastern Conference.
Brent Johnson logged 37 saves in goal for the Penguins.
Danny Cleary and Valtteri Filppula notched a goal and an assist each for the Red Wings.
Jimmy Howard yielded four goals on 15 shots before being replaced by McDonald, who turned aside 10-of-10 shots the rest of the way.