Buoyed by a midweek Champions League win over Real Madrid, Liverpool came out flying and could have wrapped the game up by halftime with a hatful of chances including two thundering Virgil van Dijk headers, one of which hit the woodwork.
The first goal came in the 12th minute after a sumptuous long pass from Trent Alexander-Arnold to Salah on the right wing. His low cross eluded Manchester City goalkeeper Stefan Ortega for Gakpo to nudge the ball in at the back post.
Salah scored Liverpool's second with a 78th-minute penalty, after his striker partner Luis Diaz was brought down by Ortega in the box, sending the Anfield crowd into delirium.