Two goals inside the opening 17 minutes were enough for Jurgen Klopp's side, as they comfortably held on against a Newcastle side that played with 10 men for three quarters of the match.
Eddie Howe's men remain fourth for now, but could drop out of the Champions League places if Tottenham Hotspur win tomorrow.
Newcastle started the game strongly and were arguably the better side throughout the game, but 15 minutes of madness cost them dearly, and the repercussions from that will be felt for their EFL Cup final versus Manchester United next weekend.
Inside ten minutes, a defensive lapse between Kieran Trippier and Fabian Schar left Nunez in acres of space, and the Uruguayan was expertly found by Trent Alexander-Arnold, before the Liverpool forward controlled well and fired home his first goal since before the World Cup break.
Moments later, another superb assist, this time from Mohamed Salah, sent Gakpo through, and despite Pope coming out to close off the angle, the Dutchman was able to squeeze his shot past him to make it 2-0.
The game then rapidly got away from Newcastle as Pope was sent off midway through the first half in bizarre circumstances.
After Trippier's poor free kick went straight into the gloves of Alisson, the goalkeeper quickly set Salah off on the break before the on-rushing Pope tried, and missed, a header and inadvertently handled the ball away from the path of the Egyptian.
Referee Anthony Taylor wasted no time in pulling out the red card for the Newcastle goalkeeper, who will now miss the EFL Cup final next weekend.
Martin Dubravka is the back-up keeper for the Magpies, but he is cup-tied for the EFL Cup, so that means that Loris Karius may have to deputise, and his last game for an English club was Liverpool's infamous Champions League final defeat to Real Madrid in 2018.
Things may have been very different had Miguel Almiron taken an early chance, but a poor first touch allowed Alisson to rush out and block his attempt.
Allan Saint-Maximin created that opportunity, and he then hit the woodwork on the half-hour mark, after a mazy run saw him force a save from Alisson who tipped it onto the post.
That would not be the last time they were denied by the frame of the goal in the first half, as Dan Burn rattled the crossbar with a header shortly before half time.
Newcastle understandably struggled to impose themselves as much in the second half as they began to tire, and Liverpool should have added a third, with Diogo Jota missing two good chances towards the end.
Callum Wilson missed a gilt-edged chance in the final 10 minutes which would have made for an interesting finale, but Alisson hung on to a well-deserved clean sheet as Liverpool ran out 2-0 winners.
Liverpool will now focus on their heavyweight clash with Real Madrid in the Champions League on Tuesday - a repeat of the final from last May.
The Reds will be out for revenge on their Spanish opponents after losing the final in Paris, and go into the game on the back of two consecutive victories.
Newcastle have a huge game on the horizon as well, as they make the trip to Wembley to face Man United in the EFL Cup final next.No Data Analysis info