Jurgen Klopp's side recovered from Harry Kane's early strike to move in front thanks to goals from Diogo Jota and Andrew Robertson.
But South Korea forward Son equalised after Alisson missed his attempt to cut out Harry Winks' pass.
Liverpool held on for a point despite having to play the final 13 minutes with 10 men following Robertson's dismissal for an ugly hack on Emerson Royal.
For the first time in four years, Liverpool won't be top of the table on Christmas Day.
The Reds are three points behind leaders Manchester City, who thrashed Newcastle 4-0 earlier on Sunday.
After winning their previous eight games in all competitions, Liverpool once again left London frustrated having lost at West Ham and drawn at Brentford this term.
The pulsating encounter was a welcome antidote to the coronavirus mayhem which has engulfed the Premier League, with six games postponed this weekend.
Tottenham had been hit the hardest by Covid, with Liverpool's visit their first game in a fortnight after matches against Rennes, Brighton and Leicester were postponed.
Nine of Conte's squad contracted the virus and some of them remain in isolation.
Liverpool weren't immune either and, just hours before kick-off, Thiago Alcantara tested positive, while Jordan Henderson was sidelined by a non-Covid illness.
Virgil Van Dijk, Fabinho and Curtis Jones remained absent having missed Thursday's win against Newcastle after testing positive.
Despite so many missing stars, Liverpool made a menacing start but Kane had the perfect response in the 13th minute.
Racing onto Tanguy Ndombele's pin-point pass into the Liverpool area, Kane guided a clinical finish into the far corner.
It was only Kane's second Premier League goal of a difficult season for the England captain, ending a six-game drought in the competition and delivering his first home league goal since May.