Nigel Adkins' side started well and came close to scoring after 20 minutes when Rickie Lambert crossed for David Connolly who headed down for Guly Do Prada but his shot was smothered by Jimmy Walker.
Saints did score in the 26th minute though when Guly drove at the Walsall defence, cut onto his right foot and curled a wonderful shot into the far corner from just inside the box.
They extended the lead when Connolly's 18-yard strike flew past the hapless Walker.
Former Arsenal trainee Julian Gray curled a tremendous shot past Kelvin Davis from just outside the box in first-half injury time to bring Walsall back into the game.
Just after the interval starlet Chamberlain came off the bench and with his first touch riffled a shot against the post from 18 yards. But after 67 minutes he bent a unstoppable effort into the top right-hand corner from 25-yards.