Jonathan Walters had put Stoke ahead shortly before the interval, heading home from close range after Xherdan Shaqiri’s cross rounded off a rapid counter-attack from the hosts after Ben Woodburn’s penalty appeal was rejected.
But a half-time double change from Jurgen Klopp turned the game on its head and boosted Liverpool’s hopes of Champions League qualification, with Coutinho and Firmino introduced at the interval.
Coutinho grabbed the equaliser with a neat finish from inside the penalty area and just two minutes later the visitors were in front in stunning fashion.
Firmino let fly with a brilliant volley that gave Lee Grant no chance and, although Simon Mignolet had to deny Saido Berahino his first Stoke goal, Klopp’s men held on for a priceless victory.
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