Danny Ings netted the opener with just four minutes gone when he turned in his first goal since October 2015 from Sadio Mane’s stellar assist.
Mohamed Salah’s expert finish on 72 minutes – a strike that equalled the Premier League record for most number of goals in a 38-game season – looked to have put the Reds on course for victory.
But West Brom reduced the arrears when Jake Livermore turned in from close range after Loris Karius had blocked Jonny Evans’ initial snap-shot at a corner.
And Salomon Rondon completed the comeback when he crashed in a header from a free-kick to ensure the points were shared in the Midlands.