The new manager’s only signing to date, Fabio Borini, opened the scoring, as his imminent second signing, Joe Allen, watched from the stands.
Pepe Reina and Luis Suarez made their first appearances under the new boss, while Lucas Leiva made his first start at Anfield since 2011 following injury. Daniel Agger sported his new ‘YNWA’ knuckle tattoo and the Kop showed their support for the Man City target.
Captain Steven Gerrard and Suarez linked up effectively – looking like the old Gerrard and Torres combination – with Suarez playing centrally, Borini left and Downing cutting inside from the right in Rodgers’ three-man attack.
It was Gerrard who scored the second shortly before half-time, with Suarez assisting as he had done for Borini to volley the opener on his Anfield debut on 21 minutes.
Glen Johnson scored a superb volley from the edge of the box midway through the second half to add a third.
It was a very comfortable and enjoyable night at Anfield for the Reds.
Goals: Borini (21), Gerrard (41), Johnson (72).
Liverpool (4-3-3): Reina, Johnson, Skrtel (Carragher 76), Agger, Enrique; Lucas Spearing 86), Shelvey (Adam 76), Gerrard; Borini, Suarez, Downing.
Subs not used: Jones, Kelly, Henderson, Carroll.