The Baggies set their stall out to make life as difficult as possible for the Reds, but Sadio Mane’s early goal had looked to be enough to secure, before Semi Ajayi stole the headlines late on.
With the visitors playing with ten men behind the ball in the opening stages, Jurgen Klopp’s team were forced to be patient, before Mane edged them ahead on 12 minutes.
Joel Matip’s long pass caught his opposite centre backs too square and Mane raced on and smashed past Sam Johnstone.
That early goal did nothing to change the flow of the match as West Brom sat in and Liverpool grew more and more frustrated.
Liverpool continued to boss everything after the break with skipper Jordan Henderson flashing an effort wide.
And with Klopp’s side unable to break through, the Baggies stayed in the game and pull off Allardyce’s masterplan with 10 to go.
Matheus Pereira’s deep corner caused problems in the Liverpool box and Ajayi got highest to nod home.
Full Time at Anfield it’s Liverpool 1 West Brom 1