Liverpool struck a potentially decisive blow in the Premier League title race as victory over reigning champions Manchester City at Anfield opened up an eight-point lead at the top of the table.
The confrontation between the two domestic superpowers had been billed as a defining moment in Liverpool's 30-year quest to land the title - and this outcome leaves them with a commanding advantage over Leicester City in second place.
Liverpool took the lead after only six minutes when Fabinho flashed a 25-yard drive past keeper Claudio Bravo, deputising for injured Ederson, the goal given after a video assistant referee check for handball against Trent Alexander-Arnold.
Manchester City were threatening in possession but Jürgen Klopp's team are ruthless in attack, as proved when Mohamed Salah doubled their lead six minutes later, heading in at the far post from Andrew Robertson's superb cross.
Raheem Sterling missed a headed chance and Sergio Agüero saw a shot deflected on to the post as City tried to find a foothold but it was all over six minutes after the break when Jordan Henderson's pinpoint delivery lured Bravo into a critical moment of hesitation and Sadio Mané headed in.
Bernardo Silva pulled one back with 12 minutes left but it was too late for City, who will rue not making the most of their plentiful possession and opportunities as they now lie nine points off the top in fourth place.
Guardiola was fuming at the final whistle, appearing to thank referee Michael Oliver sarcastically before leaving the pitch, shortly after being enraged when another penalty claim against Alexander-Arnold was waved away.
Liverpool, meanwhile, celebrated a victory that gives them a real hold at the Premier League summit.