Jetro Willems opened the scoring with a memorable goal, but Jurgen Klopp’s side fought back strongly and won 3-1 thanks to two goals from Sadio Mane and a strike from Mo Salah.
Newcastle, with Jonjo Shelvey recalled in place of the injured Sean Longstaff, got off to the perfect start.
Joelinton, holding the ball up well, played the ball out to Willems, on the left side of Liverpool’s box, and he turned inside on to his weaker right foot and lashed an unstoppable shot past Adrian.
Liverpool, however, were never going to be on the back foot for long, and, after steadying themselves, they took the game to United.
The home side looked for spaces and openings in and around the box, and had a penalty appeal waved away in the 27th-minute when Jamaal Lascelles appeared to grab Joel Matip in the box.
A minute later, Liverpool were level. Andy Robertson, once with Bruce at Hull City, skipped past Emil Krafth and crossed for Mane, who finished well.
Jurgen Klopp’s side pressed on. And on. They pressed high up the pitch and forced Newcastle into a series of mistakes. They just couldn’t keep the ball, and an error from Christian Atsu was to prove costly.
Rather than play an easy pass, Atsu got himself into trouble and was dispossessed. The ball was quickly played forward by substitute Firmino, and Mane scored into an empty net after Martin Dubravka fumbled.
Dubravka, however, kept United in the game after the break by denying Robertson and Trent Alexandar-Arnold.
Bruce sent on Yoshinori Muto and Javier Manquillo for the last 25 minutes, but there was to be no way back for Newcastle. Salah was table to take advantage of a slip from Fabian Schar to score a third goal for the Champions League-winning side in the 72nd minute.
LIVERPOOL: Adrian, Alexander-Arnold, Matip, Van Dijk, Robertson, Oxlade-Chamberlain (Milner, 74), Fabinho, Wijnaldum (Shaqiri, 84), Mane, Origi (Firmino, 36), Salah.
NEWCASTLE UNITED: Dubravka; Krafth (Manquillo, 65), Schar, Lascelles, Dummett, Willems; Almiron (Almiron, 65), Hayden, Shelvey, Atsu; Joelinton.