The result leaves Liverpool in seventh place in the standings - seven points adrift of leaders Manchester City - while Newcastle enter the international break in ninth position after Rafael Benitez extended his own personal unbeaten record against his former club to five matches.
Jonjo Shelvey was instrumental in many of Newcastle's moves against his former club and a fine pass to Matt Ritchie gave the Scot the chance to get an effort on goal, but it was too close to Simon Mignolet.
Midway through the first half, Liverpool did not know how they had not opened the scoring, with Georginio Wijnaldum having a volley strike the post and, after a goalmouth scramble, Dejan Lovren seeing a shot cleared off the line.
However, the visitors were ahead before the half-hour mark as Coutinho added another stunning goal to his growing collection, with a thunderous strike from 25 yards finding the right top corner of Rob Elliot's net.
Liverpool remained in the ascendancy but out of nowhere, Newcastle got back on level terms as Jurgen Klopp's team made another mistake in defence.
A through-ball from Shelvey found the run of Joselu and although Joel Matip got back to make a tackle after playing the Spaniard onside, he only kicked the ball against the striker and it ricocheted into the net, giving the former Stoke attacker his second goal of the campaign.
Liverpool soon went back onto the offensive but they were unable to carve out any more clear-cut openings before the break as Newcastle successfully nullified the threat offered by the likes of Mohamed Salah and Sadio Mane.
After the restart, it was Liverpool who began on the front foot and six minutes into the second half, they should have regained the lead.
After Ciaran Clark sliced his clearance into the path of Sturridge, the forward fired straight at Elliot before Salah volleyed the rebound over the crossbar.
The match soon descended into a series of mistimed challenges with Liverpool's Joe Gomez and Jordan Henderson regularly involved, and the passage of play acted as the catalyst for the quality dropping down a level.
Neither side were able to create a clear-cut chance heading into the closing stages of the game, with it taking a header from substitute Dominic Solanke to break the lull in opportunities.
Two minutes from time, fellow replacement Alex Oxlade-Chamberlain had his own chance to head home from inside the penalty area but under pressure, he directed the ball over the bar.
In added-on time, Mohamed Diame almost won it for Newcastle but after his deflected strike was saved by Mignolet, both teams had to be content with a draw on Tyneside.