It was one-way traffic in the first half as United dominated against the relegation-threatened Seagulls.
Twice in a minute they were denied by the woodwork as headers from Matt Sparrow and then Hooper hit the crossbar.
But Hooper finally fired his side in front in the 42nd minute, drilling a right-foot shot into the bottom corner for his 27th goal of the season.
Brighton were reduced to 10 men in the 79th minute when centre-back Matt Heath was sent-off for bringing down Hooper in the box.
Midfielder Grant McCann stepped up to fire the penalty past goalkeeper Mikkel Andersen and keep Scunthorpe in the play-off positions.