It means that Southampton go into the final day of the season knowing that even if they win against Sheffield United, they could still end up being relegated to League One.
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The Baggies, however, are bound for the Premier League unless they lose at QPR, Hull win at Ipswich and there is a 13-goal turnaround in their respective goal difference while Stoke pick up a point against Leicester.
That seems highly unlikely and the fans who swarmed on to the pitch at The Hawthorns at the final whistle celebrated as if they are already guaranteed to go up.
Chances began to arrive for the home side before half-time, with Jonathan Greening lashing one effort over the bar and Richard Wright denying Kevin Phillips.
The Saints had a decent shout for a penalty when Marek Sagnaowski met Jason Euell's cross but saw the ball bobble up off Neil Clement's hand.
But the visitors remained under the cosh for long periods of the second half with Ishmael Miller and Phillips forcing further saves from Wright.
Only when Lallana arrived off the bench did the Saints begin to threaten and he tested Dean Kiely with one swerving shot before running clear and thundering his shot into the bottom corner of the net.
That stunned the home side but they responded by piling on the pressure.
Clement and Luke Moore both went close with headers before Brunt collected the ball on the edge of the box and drilled his low shot through Wright's legs.
Southampton boss Nigel Pearson:
"We are disappointed not to have won after going in front but the point gives us more of a fighting chance than if we had lost.
"It drags other teams back into the equation and applies pressure on them.
"If we perform like that on Sunday we have a great chance of winning our last game and hopefully staying up."
West Brom:
Kiely, Hoefkens, Barnett, Clement, Robinson, Gera, Greening (Moore 81), Koren, Morrison (Brunt 64), Miller (Bednar 69), Phillips.
Subs Not Used: Danek, Albrechtsen.
Booked:
Hoefkens, Clement.
Goals:
Brunt 84.
Southampton:
Richard Wright, Jermaine Wright, Perry, Lucketti, Surman, Viafara, Idiakez, Safri (Dyer 62), Euell, Saganowski (Lallana 74), John (Wright-Phillips 74).
Subs Not Used: Davis, Licka.
Booked:
Euell, Perry, Idiakez.
Goals:
Lallana 77.
Att:
26,167
Ref:
Lee Mason (Lancashire).