After a close first half, in which neither side really got to grips with the match, it was AFC Bournemouth who were handed an advantage early after the restart.
Franchise FC's Belson was shown a straight red card for a professional foul on Brett Pitman in the 47th minute.
The winner came in the 77th minute when a Hollands drive was deflected off Anderton to wrong foot the Franchise keeper, and finding the back of the net.
The Cherries win through to claim their second League One scalp in this years competition.
Full match report to follow .............
AFCB: Jalal, Guyett, Cooper, Pearce, Bradbury, Cummings, Bartley, Hollands, Anderton, Goulding, Sturrock
Subs: Pryce, Ward, Partington, Pitman (for Goulding, 14 mins), McQuoid (for Sturrock, 71 mins)