Vicky Jepson’s Reds took control of the Continental Cup tie from the off, to bounce back from defeat against Sheffield United Women in their opening Group A fixture.
Niamh Charles put the visitors in front with three minutes on the clock as she guided a header home after a dangerous corner by Kirsty Linnett.
And Linnett doubled that early advantage almost immediately as she beat the goalkeeper when a shot from Rinsola Babajide fell into her path.
Coventry halved the deficit in the eighth minute as the goals kept coming, but from there Liverpool settled and they were comprehensive leaders by the break.