It marked the first Barclays FA Women's Super League goals and points of the season for Marta Tejedor’s side to move off the foot of the early standings in style.
Blues made two changes from last weekend's 5-1 win at Leicester City in the FA Women’s Continental League Cup with Hannah Hampton returning in goal and Brianna Visalli drafted in.
Buoyed by that haul the hosts started with confidence, having a series of shots and crosses charged down.
The opener soon arrived when Staniforth's bending free-kick from a central-right position was thumped to keeper Frances Kitching’s left by Harrop.
The hosts remained on top with Staniforth among those denied by last-ditch defending, her shot from the left of the area blocked by Sophie Bradley-Auckland.
Rachel Williams saw an instinctive 25-yard lob sail over with 20 minutes on the clock and Staniforth and Sarah Mayling combined to set Abbi Grant off and running but her shot was tame and easily held by Kitching.
Adrienne Jordan, who had her hands full shackling Liverpool’s most-credible threat Rinsola Babajide, guided into Staniforth to flash low across goal after half an hour, Kitching again having to be alert to push it wide.
Staniforth narrowly cleared the far post with a similar effort and Chloe Arthur tested Kitching’s concentration with an audacious 45-yard lob that had to be swatted over seconds before the interval.
Babajide’s direct run was halted by Harrop early in the second half before a shot from the loose ball flew high over the bar.
Lucy Whipp could not quite get an effort out of her feet at the other end with Grant’s swing taking an important deflection off Leighanne Robe moments later.
Liverpool had few chances of note but Blues were indebted to Hampton in the 64th minute, producing a fine double stop low to her right from substitutes Kirsty Linnett and Courtney Sweetman-Kirk in quick succession.
That instigated a brief Liverpool flurry in which Becky Jane had a shot charged down but Blues soon regained control.
Staniforth and Grant combined to tee up Mayling whose shot was smothered by Kitching and Mayling then sought to turn provider with a swinging cross that Williams nearly converted only to be denied again by the in-form visiting stopper.
The reprieve was short lived, though, with Harrop recycling the corner, sending in a looping cross that was pushed out by Kitching to Staniforth whose drive from the right of the box flew in high across goal.
Sweetman-Kirk was denied at the near post by Hampton late on but it was a comfortable finish for Blues.
Blues: Hampton, Jordan, Harrop (c), Holloway, Visalli, Staniforth, Arthur, Whipp, Grant (Walker, 88), Williams, Mayling.
Unused subs: Scott, Scofield, Simkin, Brooks (gk).
Goals: Harrop 9, Staniforth 83.
Booking: Arthur 68.
Liverpool: Kitching, Jane, Bradley-Auckland, Purfield, Robe, Roberts, Lawley (Linnett, 63), Bailey, Charles (Hodson, 79), Clarke (Sweetman-Kirk, 63), Babajide.
Unused subs: Murray, Rodgers, Kearns, Preuss (gk).
Referee: Lisa Benn.