The Reds started well, with Danny Ings scoring his first league goal in two-and-a-half years to put Jurgen Klopp's side ahead.
West Brom piled the pressure for small spells during the first half, however Liverpool dominated possession and controlled much of the proceedings to go into the break 1-0 up.
A long ball forward set Mohamed Salah and substitutes Roberto Firmino and Alex Oxlade-Chamberlain off on a brilliant counter-attack. The latter threaded a reverse pass to the Egyptian in the box, who lifted a nonchalant dink past the Baggies keeper.
The Reds' two-goal advantage was halved minutes later when they failed to clear a corner swung in from the right and after a scramble, Jake Livermore hooked the ball into the back of the net.
Salomon Rondon then equalised for the Baggies, with just two minutes remaining. The forward was first to a free-kick clipped in from the left flank as he powered a header inside the near post past Loris Karius.
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