The hosts recovered from an early setback to lead through Claudia Walker’s opportunist strike and an own goal created by Sarah Mayling’s troublesome free-kick.
And while the Red Devils had the points in the bag long before the end, Blues will no doubt reflect on what might have been had either of two glorious opportunities been taken in the second half.
Manager Carla Ward made three changes from the opening day defeat at Brighton.
Rachel Corsie and Emma Kelly were drafted in alongside new recruit Mollie Green. They replaced Jamie-Lee Napier, Chloe McCarron and Connie Scofield who were all named on the bench.
Blues got hit with an early sucker punch as Ella Toone lifted into the box from the right for Jane Ross to squeeze a deft header inside the far post.
United threatened a second when Katie Zelem played in Leah Galton but a combination of Harriet Scott’s pressure and Hannah Hampton’s swift reactions snuffed out the danger.
It was an important intervention as the hosts levelled within a minute, Walker hassling Millie Turner off the ball before keeping her cool to steer low inside the far post after Mollie Green’s pressing had initially earned back possession.
Christie Murray then picked the pocket of Katie Zelem in a similar position but Walker’s snapshot was straight at keeper Mary Earps.
Blues did not have to wait long to lead, though, with Mayling’s swirling free-kick from the left persuading Abbie McManus to get something on it, a touch that guided the ball into the back of her own net.
There was an even flow to the game but United got the equaliser nine minutes before half-time in fortuitous circumstances.
Green felt she had won the ball fairly on the edge of the area but Zelem took full advantage of the free-kick being awarded, caressing the ball over the wall to Hampton’s right.
United boss Casey Stoney shook things up at half-time with a triple substitution, ex-Blues midfielder Hayley Ladd being among those introduced, and the visitors hit the front again within two minutes of the restart.
Kirsty Hanson’s dash down the right ended with a precise daisy-cutting cross that was finished from six yards by Toone.
Blues had a similar opening at the other end just before the hour, Mayling steering in a ball that was crying out to be converted only for Kelly to fire off target from close range.
That miss was punished three minutes later as Hanson slammed home through a host of bodies from Jackie Groenen’s cutback.
Another delicious Mayling delivery found full-back Scott to thump off target at the far post, while United continued to threaten as Hanson brought the best out of Hampton who parried strongly to her right as red shirts closed in for the rebound.
The fifth arrived with 10 minutes to go when Toone seized the ball from Rebecca Holloway and Alessia Russo teed up Hanson for a tap in.
Blues: Hampton, Scott (Toussaint, 90+2), Corsie, Brougham, Holloway, Green, Whipp, Murray, Mayling, Walker, Kelly (Scofield, 65).
Subs: Napier, Grant, McCarron, Lawley, Maguire (g/k).
Goals: Walker 14, McManus (og) 27.
Man United: Earps, Ross (Russo, h-t), McManus (Turner, h-t), Batlle, Toone, Groenen, Turner, Zelem (Ladd, h-t), Smith, Hanson, Galton.
Subs: Okvist, Hornby, Ramsey (g/k).
Goals: Ross 5, Zelem 36, Toone 47, Hanson 60, 80.
Referee: Lucy Oliver.