Casemiro opened the scoring when heading in a Luke Shaw free-kick and the lead was doubled before the interval when Marcus Rashford's shot looped in off Sven Botman, eventually going down as own goal by the Dutch defender.
In a rather scrappy second half, Newcastle had more of the game as they tried to retrieve the situation but Loris Karius was still the busier of the two keepers, as the Reds continued to threaten on the break, even if David De Gea did have to make one late stop, from Joelinton, in stoppage time.
In the dying seconds, Bruno Fernandes should have added a third but Karius pulled off a miraculous save.