Joe Willock scored a dramatic 95th-minute equaliser for Newcastle to put a serious dent in Jurgen Klopp's hopes of finishing this season in the top four.
Liverpool led through Mo Salah's 20th league goal of the season after only three minutes but were then frustrated by an outstanding display from visiting goalkeeper Martin Dubravka.
But in an astonishing collapse in injury time, Liverpool were fortunate when Callum Wilson had an equaliser ruled out for handball before Willock was given time in the arsa to shoot home via a heavy deflection off Fabinho.
Now that Liverpool have to qualify for the Champions League through their own efforts, Klopp was indebted early on to Salah.