Southampton failed to convert a host of chances that would have seen them climb out of the Premiership relegation zone.
Camara (right) was a thorn in West Brom's side
Henri Camara caused West Brom trouble throughout and came close to breaking the deadlock when he stabbed Peter Crouch's header on to the post.
Nigel Quashie had a shot saved from close range before David Prutton guided a volley over from six yards late on.
Kieran Richardson had West Brom's best chance when he hit the crossbar with a curving, long-range first-half effort.
In a contest between the team with the worst Premiership home record and visitors with the worst return on the road, the lack of goals should have come as no surprise.
But in an open game, it was not for the want of trying.
The occasion was riddled with nerves and the tension showed in a match littered with lazy passing and wrong options.
And the edginess spread to the stands as time ticked down with West Brom pushing forward for a late winner.
It would have been ill-deserved against a well-organised Saints side.
Baggies boss Bryan Robson had showed attacking ambition in loading his midfield with free-running ball players, but it failed to translate from paper to pitch.
Only Richardson lived up to the billing, seeing a free-kick tipped over and a wickedly, curving shot cannon back off the crossbar.
West Brom enjoyed all the early possession but were unable to prise open their opponents and, slowly but surely, Southampton drew the sting from their hosts and grew into the game.
Camara proved a constant menace to the Baggies back four.
He hit the post and saw a free-header tipped over by the otherwise hesitant Russell Hoult in goal in the first half, both chances coming from teasing Graeme Le Saux crosses.
After the break Camara created a glorious opportunity, breaking down the left, rounding Thomas Gaardsoe and cutting inside Neil Clement only to blaze a shot over.
Hoult made another telling save to keep it all square when he stood up to parry Quashie's powerful shot after the Scot broke into the area.
Quashie then linked with Olivier Bernard on the right before the Frenchman dinked a cross to the far post which Prutton volleyed over from six yards with the goal gaping.
Baggies boss Bryan Robson
"It makes it (staying up) a harder task but we've got to keep going and we're going along the right lines.
"It was not as good as we have been playing. Our passing was poor and maybe the occasion got to some of the players.
"We had the better chances in the first half but after the break Southampton could have won it."
Saints boss Harry Redknapp
"I've seen a massive improvement in my time here and I was well-pleased with how we played.
"We didn't win it through missed opportunities. We created gilt-edged chances which we should have put away.
"They worked hard, it was encouraging and if we continue to play like that we'll be okay."
West Brom: Hoult, Albrechtsen, Gaardsoe, Clement, Robinson, Gera (Scimeca 81), Wallwork, Richardson (Koumas 74), Greening, Campbell, Earnshaw.
Subs Not Used: Purse, Horsfield, Kuszczak.
Booked: Richardson, Gera.
Southampton: Smith, Delap, Lundekvam, Jakobsson, Bernard, Prutton, Redknapp, Quashie, Le Saux, Camara, Crouch.
Subs Not Used: Phillips, Higginbotham, Poke, Telfer, Davenport.
Booked: Delap, Bernard, Redknapp.
Ref: M Riley (W Yorkshire).