Magpies goalkeeper Nick Pope was sent off and will consequently miss the Carabao Cup final against Manchester United next week through suspension.
However, despite a promising start, the Magpies went behind just 10 minutes in as Darwin Núñez touched down Trent Alexander-Arnold’s exquisite pass and emphatically finished.
The Reds hadn’t lost any of the Uruguayan’s previous six goalscoring games and doubled their lead just seven minutes later, with Cody Gakpo latching onto Mohamed Salah’s superb pass to score his second in as many games.
After Elliot Anderson was sacrificed 24 minutes into his first PL start, substitute goalkeeper Martin Dúbravka immediately dealt with a header from Gakpo.
Saint-Maximin continued to provide inspiration as the second half started and found Alexander Isak in the box, although the striker couldn’t find the target with his shot on the turn.
Núñez provided a reminder of Liverpool’s threat in behind, cutting in and forcing Dúbravka into a strong save, although the forward then departed holding his shoulder, while Eddie Howe later took Joelinton off when it appeared there could be a problem for the Brazilian.
While the Magpies can look forward to the Carabao Cup final, they will also be looking over their shoulder in the league with Liverpool six points behind them having played a game less in the race for the top-four.
