Brian Stock stung home keeper Keiren Westwood's palms with a fierce early shot, while Grant Smith had an effort deflected wide at the other end.

But Graham got the winner when he turned in Cleveland Taylor's cross.

Despite dominating possession, Rovers were unable to break down a formidable Cumbrian defence in the second half, with Peter Murphy outstanding.

Carlisle: Westwood, Raven, Murphy, Livesey, Horwood (Arnison 89), Taylor, Bridge-Wilkinson, Grant Smith, Hackney, Graham (Jeff Smith 83), Garner (Dobie 87).
Subs Not Used: Howarth, Carlton.

Booked: Hackney.

Goals: Graham 40.

Doncaster: Sullivan, O'Connor (Mills 86), Stephen Roberts, Lockwood, Gareth Roberts, Stock, Wellens, Green, Price (Heffernan 65), McCammon (Elliott 77), Coppinger.
Subs Not Used: Wilson, McDaid.

Att: 8,390.

Ref: Lee Probert (Wiltshire).