Liverpool took the lead on four minutes, Danny Ings scoring his first Premier League goal since 2015 with a close-range finish.
Mohamed Salah extended Liverpool's lead on 72 minutes, latching on to an Alex Oxlade-Chamberlain through-ball to chip Ben Foster.
It's his 31st PL goal this campaign, which means he now shares the record for goals in a 38-match season.
But Livermore got a goal back for West Brom on 79 minutes, scrambling the ball in following a corner, before Rondon headed in a Chris Brunt free-kick at the near post with two minutes left to draw the hosts level.
West Brom remain bottom on 25 points, eight points from safety with three matches left, while Liverpool are third with 71 points, three behind Manchester United.
West Brom: 28 April v Newcastle (A)
Liverpool: 28 April v Stoke City (H)