The striker arrived on loan from Charlton Athletic on Friday and scored the winner in the 79th minute when he rifled the ball into the bottom left-hand corner of the goal from 18 yards after his initial effort was blocked.
But the 20-year-old, whose original move to Roots Hall for £200,000 was abandoned during the transfer window when a medical revealed a heart abnormality, blew a chance to double his tally four minutes later hen he fired wide with the goal at his mercy.
Relegation-threatened Bournemouth, who were docked ten points after going into administration, should have gone in front when Jo Kuffour won possession and teed up Sam Vokes but he blasted over when well placed.
The Shrimpers took the lead after ten minutes when Simon Francis' long ball allowed Lee Barnard to nip in behind a static Cherries rearguard and slot past Gareth Stewart for his third goal in four starts since signing from Spurs.
Mark Gower should have doubled the advantage in the 14th minute but his shot hit the left post and was cleared.
Danny Hollands had the Cherries' first shot on target but it failed to trouble Darryl Flahavan.
Bournemouth equalised when Warren Cummings' cross from a Max-Alain Gradel short-corner was met 12-yards out by Jason Pearce, who jumped highest to head past Flahavan.
The Shrimpers saw Nicky Bailey's 25-yard effort saved by Stewart and Tommy Black fired just over the bar, but then Walker came on to grab the points and add to Bournemouth's problems.