The opening quarter-hour was frantic, with tackles flying in and both sets of players showing their determination. Newcastle looked the more dangerous side, but Nick Pope was called into action to deny Florian Wirtz's curling effort. Anthony Gordon had several opportunities to score, but his efforts never found the target.
Momentum seemed to be with Newcastle, but Liverpool's Gravenberch scored a goal from 30 yards, making it 36 successive league games in which the team has scored. The Magpies' good work was undone, and their task of holding onto the lead became easier when Gordon was dismissed for a dangerous tackle on Virgil van Dijk.
Down to 10 men, Newcastle would have wanted to keep the game tight, but there was no hope of that as Liverpool doubled their lead within 20 seconds of the restart. Cody Gakpo's blocked shot fell to Hugo Ekitike, who produced a sublime finish into the bottom corner.
Newcastle refused to give up and cut the deficit on 57 minutes when Tino Livramento's cross was nodded home by Bruno Guimarães. The Magpies rallied in the closing stages and snatched a leveller in the 88th minute, with William Osula poking the ball past Alisson.
However, a late substitute had the final say when, in the 100th minute, Rio Ngumoha pounced on Mohamed Salah's low cross to curl into the corner and snatch all three points for Liverpool.