Blues created numerous chances but could not find a way through in swirling wind at Eppleton Colliery Welfare until Staniforth’s 20-yard effort from left of centre squirmed through the gloves of keeper Claudia Moan five minutes from time.
Staniforth was sent off for her celebration before the restart, an incident that also saw a supporter ejected at the request of referee Elizabeth Simms but 10-strong Blues saw through victory comfortably enough.
Manager Marta Tejedor made six changes from the 2-0 league defeat at Chelsea on Wednesday.
Harriet Scott and Connie Scofield came in for Adrienne Jordan and Chloe Arthur, both of whom missed out with minor injuries.
Goalkeeper Alex Brooks, defender Rebecca Holloway and attacking options Emma Kelly and Claudia Walker also got nods with Hannah Hampton, Georgia Brougham, Lucy Whipp and Abbi Grant on the bench.
With a strong wind at their backs Blues began with a flourish, flashing crosses in with Rachel Williams and Brianna Visalli a fraction away from connecting with Scott’s second-minute centre.
Walker’s low bouncing shot skipped just past the near post after tenacious work from a short corner by Staniforth and Kerys Harrop recycled another set piece that just evaded Williams.
Sunderland steadied the ship from there but Blues again went agonisingly close when Staniforth’s lifted free-kick skimmed off Holloway’s head in front of goal.
That instigated another Blues flurry with Scott driving across goal before Staniforth’s outswinging shot had to be clawed away from the top right corner by keeper Claudia Moan.
Williams powered through and laid off for Emma Kelly to fire narrowly high and wide of the near post and Mayling wanted a penalty having become entangled with two Black Cats having forced her way into the box.
Staniforth’s dipping free-kick was almost spilled to Williams and then the England midfielder spurned the chance of the half, scooping over from eight yards, although the ball did fly at her as she attempted to adjust.
With the wind Sunderland mustered more moments, Georgia Gibson and Keira Ramshaw having shots charged down in quick succession five minutes after the restart.
Blues kept probing with Staniforth finding Walker who was unfortunate not to net with a rasping 20-yard hit that was pawed over by the single glove of Moan.
Walker then brushed off Louise Griffiths to get in one-on-one but having beaten Moan saw her shot fizz past the far post.
The pressure kept coming but Williams could not convert with a stooping header from Mayling’s low centre.
Buoyed by staying in the game, Sunderland had a go back with Neve Herron bending narrowly wide of the top far corner from the left corner of the box and Bridget Galloway clearing the bar under pressure having been found by the lively Mollie Lambert.
Harrop was called upon to produce a last-ditch tackle to prevent Galloway getting a free run at goal and at the other end Staniforth cleared the bar from 20 yards.
Another 20-yard dipper from Staniforth was shovelled wide by Moan as the clock started ticking away but she was not to be denied.
Williams was caught by Ramshaw on the left edge of the box and Staniforth’s firm free-kick slipped through Moan’s gloves to hand Blues the breakthrough.
The delay while the supporter was being escorted out led to eight minutes added time which Blues saw through relatively comfortably, Brooks staying alert to gather a high ball Ramshaw had tried to attack at the death.
Sunderland: Moan, Herron (Barker 72), Potts, Griffiths, Ramshaw, Lambert, Galloway, Gibson, Beer, McCatty, Farrugia.
Unused subs: Mullen, Warren, Woolston, Cowling (g/k).
Booking: Ramshaw 84.
Blues: Brooks, Scott, Harrop, Holloway, Mayling (Brougham 90+8), Scofield (Whipp 62), Staniforth, Kelly (Grant 62), Williams, Visalli, Walker.
Unused sub: Hampton (g/k).
Goal: Staniforth 85.
Booking: Scott 55.
Sent off: Staniforth 86.
Referee: Elizabeth Simms.