Lee Bradbury got off the mark with his first Bournemouth goal following a cross from Jo Kuffour as early as the 3rd minute.
One became two for the Cherries just 5 minutes later when Bardbury netted for a second time, this time volleying home a Gradel cross past a hapless Ince in the Walsall goal.
Other chances came and went for Anderton, Bradbury, Kuffour and Gowling, but it was not to be as the Cherries secured a place in the second round of the competition.
AFCB: Begovic, Young, Perrett, Gowling, Cummings, O'Connor, Anderton, Telfer, Gradel, Kuffour, Bradbury
Subs: Moss, Pearce, Christophe, Hollands (on for Anderton, HT), Pitman (on for O'Connor, 65)