Nigerian international Peter Odemwingie's strike proved to be the decider in a rare attack from West Brom who were camped in their own half for the majority of the fixture which invited pressure from Liverpool. Glen Johnson was the culprit of lackadaisical defending as the full-back squandered possession near his own box, which allowed the Nigeria international to eventually race clear and steer the ball past Pepe Reina.
Liverpool had the chance to take the lead after 10 minutes as Luis Suarez picked out an unmarked Dirk Kuyt inside the West Brom box, but the Dutchman screwed his shot across Ben Foster and past the West Brom goal.
Dalglish's men spurned their second opportunity of the afternoon as Suarez found space on Liverpool's right and flashed an inviting ball across the face of West Brom's goal which eluded his team-mates.
The hosts continued their pressure and saw a penalty claim turned down moments later as Maxi Rodriguez was brought down by Billy Jones inside the box. Contact was minimal and the Argentine appeared to have played for the decision after running out of space with the ball.
The visitors were subdued for large parts of the opening half but could have opened the scoring against the run of play had it not been for a fantastic save from Reina.
Shane Long beat Daniel Agger in the air and the striker's cushioned header was met with a low drive from Christ Brunt but the Liverpool goalkeeper, on his return from a three-game suspension, displayed superb agility to palm the ball away.
West Brom quickly reverted back to their defensive mentality but Liverpool continued in their struggle to test Foster. Agger was another culprit of passing up a chance to break the deadlock as his shot from close range was blocked.
Shades of Liverpool's inability to finishes chances in the first half surfaced early after the restart as Suarez, who enjoyed a busy opening 45, flashed the ball across West Brom's six-yard box which failed to get a connection from anybody.
Jordan Henderson was the next candidate to go close for Liverpool. A slick one-touch interchange on the right flank which was conducted by Suarez eventually saw Andy Carroll lay the ball off for the 21-year-old, whose well-struck shot beat Foster but rebounded off the crossbar.
West Brom offered little retaliation and their vulnerability on both flanks was tested once more as Suarez found Kuyt in space inside the visitors' box but the Dutchman, in a replica scenario to the first half, pulled his shot across Foster but his effort this time hit the post.
Liverpool were fired a warning minutes later however, as Long was found unmarked inside the hosts' box but the striker had his back to goal and bizarrely opted to play a pass back outside the area, rather than turning and testing Reina.
But a rare West Brom foray forward was greeted with further pressure from Liverpool, who saw two chances fall to Carroll and Jay Spearing in a goalmouth scramble although both were blocked on the line.
Liverpool's failure to convert opportunities into goals was finally punished by West Brom as Hodgson's men took the lead with 15 minutes remaining.
Glen Johnson had successfully read Youssuf Mulumbu's stepover down West Brom's left but the Liverpool defender tried to flick the ball past the midfielder after regaining possession, which allowed the Congo international to feed a pass to Odemwingie, who raced clear and finished neatly past Reina.
A slight consolation for Liverpool will be the fact that West Brom didn't double their lead late on, as a free-kick pumped into their area was met by Paul Scharner, who had headed the ball into the net but clattered into Reina in the process.
The win for West Brom puts them into 10th, while Liverpool neglected the chance to overtake neighbours Everton and proved that any European dreams next season will be dependent on a revival of their home form.