Marquis hit his 16th goal of the season when his deflected shot from close range crept past Gills goalkeeper Tomas Holy.
Only a scuffed shot from the Rovers striker following Herbie Kane’s short corner prevented him from making it 2-0 in first-half stoppage time.
On-loan striker Mallik Wilks, who threatened throughout for the visitors, capitalised on a mix-up between Holy and Connor Ogilvie to double their advantage nine minutes after the break.
Manager Grant McCann’s side sealed their sixth away league victory of the season when Danny Andrew’s 20-yard volley beat unsighted Holy for his first league goal for Rovers.
Having beaten league leaders Portsmouth on Wednesday, the Gills managed just one shot on goal before Callum Reilly’s deflected consolation goal two minutes from time.
James Coppinger (foot) and Paul Taylor (illness) missed the Gills game, but could return for tomorrow’s visit of Rochdale.
“We were a little bit patched up, but we showed that we can call in others to come and do a job for us,” McCann said. “We’ll have to leave it until the last minute for the Rochdale game to see how many bodies we have.
“We think James Coppinger might be okay. He wasn’t too bad and after a couple of days rest he might be okay.
“It was just his foot. He just rolled it at Fleetwood and it’s not too bad. If it had been the play-off final on Saturday, Copps would have played.”
Gillingham: Holy, Fuller (O’Neill 59), Lacey, Zakuani, Ogilvie, Parrett (Bingham 26), Reilly, Byrne, Parker, Hanlan (Eaves 46), List. Unused substitutes: Garmston, M’Bo, Rees, Hadler.
Doncaster: Lawlor, Blair, T Anderson, Butler, Andrew, Rowe (J Anderson 85),Whiteman, Kane, Wilks (Crawford 77), Marquis, May (Boocock 90). Unused substitutes: Marosi, Blaney, Lund, Gibbons.
Referee: N Hair (Cambridgeshire).