James Milner's stoppage-time penalty just about extended Liverpool's unbeaten run, while Aston Villa hit five past Norwich and Marco Silva endured another loss.
Premier League results
Liverpool 2-1 Leicester
Liverpool extended their lead at the top of the Premier League table in dramatic fashion as they beat high-flying Leicester 2-1.
Of all people, it looked like Brendan Rodgers was going to end Liverpool's winning run at 16 games as the visitors drew level with the Reds thanks to James Maddison's goal eight minutes from time at Anfield.
Sadio Mane had put the home side ahead five minutes before half-time with this 50th Premier League goal for Liverpool - but all the drama was to come late on in an end-to-end finish to the game.
First, Maddison drew the visitors level, Liverpool having wasted chances to put the game to bed, before Marc Albrighton's foul on Mane allowed James Milner to nervelessly convert a penalty in the fifth minute of time added on.
Credit to Rodgers for encouraging his side to go for three points, but the Foxes return home with nothing after Liverpool made it 17 wins on the spin to move eight points clear of Manchester City, who play Wolves on Sunday.
Norwich 1-5 Aston Villa
Aston Villa went goal crazy at Carrow Road against fellow newcomers Norwich, with summer signing Wesley scoring twice and missing a penalty in a dominant first-half performance.
Jack Grealish effectively ended the contest four minutes after the break before Conor Hourihane turned the win into a rout with a fourth, followed late on by a fifth from substitute Douglas Luiz
Josip Drmic at least got Norwich on the scoresheet three minutes from the end but that was a mere consolation for punters backing both teams to score in the game rather than anything to note for Norwich, who drop to 18th as Villa leapfrog them and climb to 14th.
Brighton 3-0 Tottenham
Brighton teenager Aaron Connolly scored twice on his first premier League start as Tottenham’s nightmare run continued on the south coast with an emphatic 3-0 defeat.
It was meant to be Tottenham’s bounce back game after their 7-2 Champions League humiliation against Bayern Munich, but after gifting Brighton the opener after just three minutes they lurched from one disaster to another.
That included losing Hugo Lloris to what looked to be a serious arm injury, one suffered as he made a mess of a high, floating cross which allowed Brighton to take the lead.
Graham Potter’s Brighton were the better side throughout, first to every ball, winning almost every tackle and producing far more cutting edge than Mauricio Pochettino’s stumbling Spurs, who produced another lacklustre showing that will only add to their manager’s frustrations.