The Lions' pursuit of a top-six finish had stuttered with just two victories in eight league matches but Morison's 62nd-minute strike and a Pat Baldwin own goal sealed the points.
It was the visitors who came closest to opening the scoring and Jo Kuffour was denied his ninth goal of the season by the inside of the post before David Forde produced a stunning save to push Chris Lines' free-kick onto the bar.
The Lions regained control after the break and had two penalty appeals waved away early on while Lewis Grabban shot wide.
And their pressure paid off when Morison delightfully lifted David Martin's cross over centre-back Danny Coles before volleying past the advancing Mikkel Andersen.
Mark Wright had his shot cleared off the line as Rovers searched for an equaliser before Morison's stoppage-time shot was parried by Andersen into the path of Baldwin who could only watch as it rolled over the line.