Juergen Klopp fielded a second-string side with one eye on next week's Europa League final against Sevilla, which is now Liverpool's only route back into continental competition next season after they finished eighth in the table with 60 points.
West Brom, who are 14th on 43, took the lead in the 13th minute when 17-year-old Jonathan Leko slipped the ball to the unmarked Salomon Rondon who held off a challenge and fired low past Liverpool's stand-in keeper Adam Bogdan.
The visitors were level, however, eight minutes later when Jordon Ibe scampered half the length of the pitch before burying a low shot into the bottom corner for his first league goal of the season.
(Reporting by Toby Davis; editing by Ed Osmond)
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