Sadio Mane scored twice and Mohamed Salah netted the third as the Reds recovered from an early blow in the first fixture since the international break.
Jetro Willems had put the Magpies ahead with a fine strike after seven minutes until Mane's superb curling effort midway through the first half restored parity.
The speedster grabbed his second of the match shortly prior to half-time as Salah then added the third 20 minutes from time to maintain the Reds' 100 per cent start to 2019-20.
Team news
Alex Oxlade-Chamberlain made his first Anfield start since April 2018, while Divock Origi also appeared in the starting XI.