Leicester were always a threat on the break and looked to have secured a point when James Maddison equalised 10 minutes from time .
A stoppage-time James Milner penalty sparked huge celebrations at Anfield as Liverpool beat Leicester City 2-1 on Saturday for an eighth successive Premier League win that moved them eight points clear at the top of the table.
The contrast with Tottenham Hotspur, whom they beat in last season's Champions League final, could not be more marked as Mauricio Pochettino's side continued to ship goals in a 3-0 loss at Brighton & Hove Albion while Aston Villa thumped Norwich City 5-1 and Burnley edged Everton 1-0.
With Manchester City not playing until Sunday, Liverpool looked determined to lay down their marker and were well in control when Sadio Mane scored the opener — his 50th league goal for the club — after getting on the end of a superb through ball from Milner.
But Leicester were always a threat on the break and looked to have secured a point when James Maddison equalised 10 minutes from time before a rash Mark Albrighton challenge on Mane set up Milner's penalty chance.
"We had to dig deep and find the points," said Milner, who said he just had to concentrate and stay calm to convert his 16th spot-kick in 18 attempts for Liverpool.
"The boys have done it time and time again. There was a few tired legs and it was about getting the result."
The game ended with several players from both sides confronting each other as passions threatened to boil over.
Tottenham's defeat at the Amex stadium was compounded by a horror injury to keeper Hugo Lloris, who was taken to hospital after injuring his arm in trying to keep out Neal Maupay's opener on three minutes.
The French keeper, who made a howler against Southampton last week and conceded seven against Bayern Munich, was badly at fault in parrying the ball straight into Maupay's path.
But recriminations were soon forgotten as the severity of his injury became clear and Lloris was treated on the pitch for six minutes before leaving on a stretcher.
Pochettino said the injury so early in the game affected the rest of the team although questions remain about another substandard Spurs performance so soon after their mauling by Bayern.
Brighton's other goals were scored by 19-year-old Irish striker Aaron Connolly in his first Premier League start.
"I've been watching the Premier League since I was four or five, so to be playing in it now, and then to score and to win 3-0, it really is a dream come true," Connolly said.
Brazilian striker Wesley scored twice for Aston Villa in the 5-1 win over Norwich although he spurned the chance of a first-half hat-trick by missing a penalty.
That hardly mattered as Villa recorded their highest away Premier League win in 11 years against a side who had conquered Manchester City in their previous home game.
Everton sit one point above Norwich after their fourth successive league defeat, a result that will pile more pressure on manager Marco Silva. Jeff Hendrick scored Burnley's winner and Everton will rue the dismissal of Seamus Coleman for two yellow cards.
Bottom side Watford remained without a Premier League win this season after being held to a goalless draw by Sheffield United at Vicarage Road.
West Ham United entertain Crystal Palace in Saturday's late game.