Jurgen Klopp’s side led at St James’ Park through Philippe Coutinho's brilliant goal on 29 minutes.
Newcastle levelled seven minutes later when Jonjo Shelvey played in Joselu, who scored when Joel Matip’s tackle deflected off him into the net.
After the break, Daniel Sturridge and Mohamed Salah failed to punish Ciaran Clark’s miskick, while Shelvey cleared Dejan Lovren’s header off the line.
Two Liverpool substitutes, Dominic Solanke and Alex Oxlade-Chamberlain, both put headed chances off target.
In stoppage time, Newcastle substitute Mohamed Diame had a chance for the winner, but his shot deflected into the arms of Simon Mignolet.
Liverpool fall to seventh, while Newcastle rise to ninth.