Trent Alexander-Arnold came off the bench to score the only goal 14 minutes from time as the Reds moved to the brink of a record-equalling 20th English top-flight title.
Liverpool could be crowned champions on Wednesday should Arsenal lose at home to Crystal Palace. If the Gunners avoid defeat, Arne Slot's men have the chance to seal the deal when Tottenham visit Anfield next Sunday.
Leicester have not scored a single goal at home since December as nine consecutive defeats at the King Power have taken Ruud van Nistelrooy's men down. A Liverpool cruise seemed in store when Mohamed Salah hit both posts with a glorious chance inside the first two minutes.
But after storming clear of the chasing pack in Slot's early months in charge to build a near-unassailable lead, Liverpool have slowed in recent weeks as the finish line approaches.