Roberto Firmino celebrates after grabbing the decisive goal for Liverpool against Stoke. Photo: Darren Staples, Reuters

Liverpool produced a stunning fightback as goals from surprise substitutes Philippe Coutinho and Roberto Firmino earned a precious 2-1 victory at Stoke City on Saturday.

Jurgen Klopp’s side’s hopes of finishing in the Premier League’s top-four looked set for a damaging blow when Stoke took the lead through Jonathan Walters just before halftime.

The visitors had been subdued in the opening half, barely threatening Stoke’s goal, but the introduction of Brazilian duo Coutinho and Firmino at halftime changed everything.

Coutinho equalised with 20 minutes remaining when he shot through a crowded penalty area, and three minutes later, Firmino’s superb lob put Liverpool ahead.

Almost immediately the visitors were indebted to goalkeeper Simon Mignolet, who denied Saido Berahino from close range with an incredible save.

Third-placed Liverpool held on to move nine points clear of fifth and sixth-placed Arsenal and Manchester United, both of whom have three games in hand over Klopp’s side.