Mandeville netted 13 minutes from time from the spot to earn Rovers a reprieve following a disappointing New Year’s Eve performance.
Matt Green had given the industrious hosts a deserved lead on the hour mark after Rovers manager Darren Ferguson had kept faith with the side that started in the win over Notts County.
Rovers were given much more space than they had been five days earlier at Notts County, but were unable to make it pay.
Their passing was, on occasion, careless and over-deliberation brought several promising-looking attacks to an end.
Mansfield wanted a penalty when Andy Butler clattered into Danny Rose, but the flag was already up for offside and the appeals were negated.
Rovers reverted to a back three, which had served them so well at Notts County, but quickly found themselves adrift.
Malvind Benning tried his luck from 25 yards and the ball was deflected home, with Green claiming credit for the last touch.
However, Rovers were allowed a chance to restore parity when they were awarded a penalty on 77 minutes.
Mandeville forced the advancing Scott Shearer into a fine save, but Mansfield’s goalkeeper then felled Matty Blair and Mandeville sent him the wrong way with his spot-kick.
Mansfield Town: Shearer, Bennett, Howkins, Pearce, Bennett, Collins, Baxendale (Hurst 87), Hamilton, Clements (M Rose 87), Green, D Rose (Hoban 79). Unused substitutes: Jensen, Thomas, Hemmings, McGuire.
Doncaster Rovers: Marosi, Alcock (Middleton 63), Baudry, Butler, Mason, Houghton, Blair, Rowe, Mandeville (Keegan 85), Marquis, Williams. Unused substitutes: Jones, Wright, Calder, Beestin, Longbottom.
Referee: Stephen Martin (Staffordshire).