On the stroke of half-time, Rovers defender Jerel Ifil was sent off for fouling Romain Vincelot on the edge of the box and Green's perfectly struck free-kick from 20 yards punished the offence further.
Green supplied the right-wing corner for Vincelot to head home unmarked without even having to jump six minutes from time.
The home side hit the crossbar through Chris Lines in the first half but were generally out-battled by their determined opponents.
Rovers goalkeeper Conrad Logan saved well from substitute Bas Savage in the 71st minute to prevent an even heavier defeat.
The drop beckons for Rovers, who have won only twice in 13 games under manager Dave Penney.
Source: PA
Source: PA