Lucas Moura's second-half goal cancelled out Roberto Firmino's opener to leave the Reds facing the prospect of being behind Manchester City on goal difference, only for Toby Alderweireld to turn the ball into his own net in the 90th minute when Lloris failed to hold a Mohamed Salah header.
With City beating Fulham comfortably on Saturday, Jurgen Klopp's side were in need of a positive result to keep the pressure on the champions, who play again at home to Cardiff City on Wednesday.
It looked as though Lucas' first league goal of 2019 would be enough to secure the visitors a valuable point in their top-four chase and give City the boost they wanted, only for Lloris to throw away the result.
The only shot on target of the first half proved the difference at the interval, with Firmino running into the space between Spurs' centre-back trio to head in Andrew Robertson's precise cross.
Spurs did threaten, though, even if Alisson's goal was untroubled, with Lucas and Dele Alli each coming close with efforts from the edge of the box.
Alisson had to parry a Harry Kane strike before Christian Eriksen's follow-up was blocked by Robertson as Spurs stepped up the pressure after the break.
Salah then wasted a good chance on the break for Liverpool and Spurs punished their hosts 70 minutes in, when Eriksen's scuffed effort from Kieran Trippier's cut-back was fired beyond Alisson by the arriving Lucas.
The visitors should have won it themselves inside the final five minutes, but Moussa Sissoko blasted over the crossbar after being sent clear by Son Heung-min's smart lay-off.
And Liverpool made them pay as the game ticked towards injury time, when Salah headed Trent Alexander-Arnold's looping cross goalwards and Lloris could only push the ball off Alderweireld and over the line.
Liverpool's title challenge gets a massive lift
City would have stayed top on goal difference had this finished level, but Liverpool are now two points clear of their title rivals, albeit having played a game more.
It means City will be feeling a little more pressure when they host Cardiff in midweek, even if the title race remains in their hands.
For Spurs, this could be a damaging blow to their top-four hopes. They are above fourth-place Manchester United on goal difference only and will be overtaken by Arsenal if the Gunners beat Newcastle United on Monday. Chelsea, meanwhile, are just a point further back.
