Carl Brown opened the scoring for Paul Collicutt’s side in the third minute, with Mann the provider.
Kevin Sawyer saved well from Matt McDonald in the 22nd minute as Cinderford responded well to falling behind early on.
They deservedly equalised in the 25th minute when former Evesham defender Nick Rhodes found the net.
Dunbar, who has been in fine form for the Under-21s this season, went on in place of the injured Jordan Bryan just after Cinderford levelled.
Robbie Atkinson set up Lewis Bamford 10 minutes before half-time, but Sawyer saved well again.
And Mann made it 2-1 in the 41st minute with a deflected shot which looped over goalkeeper Eric Edge and into the net.
Cinderford had a chance to make it 2-2 when Mat Liddiard tripped Bamford in the box, but ex-Evesham man Dan MacDonald saw his spot kick brilliant saved by Sawyer, diving to his left and pushing it to safety.
Substitute Nick Harrhy was close with a shot which flew just past the left post.
Mann was forced off in the 80th minute due to having something in his eye from a work related incident and he ended up in hospital.
Dunbar rounded off the scoring in the 84th minute with a fine finish after a ball in from Lewis Binns on the left.
Evesham United: K Sawyer; A Lewis, W Wellon, M Bennett; J Bryan (E Dunbar 26), A Haskayne, M Liddiard, J Turley, L Binns; A Mann (A Williams 80), C Brown. Subs not used: L Powell.
Report by Gloucestershire Echo