The Netherlands midfielder maintained his fine start to the season with a top midfield performance at Anfield, where he came away with a goal and an assist.
Earning an 8.4 player rating, Gravenberch netted the opener with a clever hooked finish over Jordan Pickford, then turned provider for Hugo Ekitike with a defence-splitting pass.
It meant he became the youngest player ever to score and assist in a Merseyside derby, aged 23 years and 127 days.
Table-toppers Liverpool are next in League Cup action when they host Championship side Southampton in the third round on Tuesday.