Former Blue White struck within the opening minute with Walsh stifling any hope of a comeback from 25 yards midway through the second half.
Despite finding it tough to get up the pitch at times, the hosts had their moments and were boosted by captain Kerys Harrop coming through a 15-minute comeback from injury unscathed.
Manager Marta Tejedor stuck with the same starting XI that kicked off the 1-0 defeat at Reading seven days earlier with Harrop on the bench but Blues endured the worst possible start as the match kicked off with scything move.
Jill Scott was picked out in the right of the box to steer into White who slid in with a looping finish which dropped inside the far post.
While that stifled the hosts in terms of territory, there was no onslaught with little action until White dispossessed Chloe Arthur in a dangerous area but the Blues midfielder recovered to cut out the one-two with Pauline Bremer.
A dipping 25-yard effort from Lucy Staniforth on the break had to be shovelled out by Ellie Roebuck with Citizens skipper Steph Houghton on hand to clear the danger.
At the other end, Lauren Hemp’s surge forward teed up Bremer to blast narrowly wide with half an hour played and from there Nick Cushing’s side really began to probe.
Janine Beckie’s inviting cross was scooped over by White from close range, while Bremer almost pounced on a short back pass from Arthur that was just about dealt with by Blues keeper Hannah Hampton.
Another Beckie cross was just behind White who could only fire wide while adjusting and Bremer’s effort was deflected wide from Caroline Weir’s corner.
Walsh then fired through a host of bodies with Hampton producing an excellent one-handed stop having been deceived by a deflection and the Blues custodian then smothered at the feet of Gemma Bonner from the next set piece.
Having weathered that storm Blues began the second half with promise, a swinging Staniforth corner met by Rachel Williams at the far post but Roebuck gathered the firm downward header.
There was a close shave when Bonner’s header back across goal from a Weir corner had to be cleared off the line by Lucy Whipp and Weir then had a swing at a loose ball from distance but it swerved just past the post at the last.
Blues carried more threat on the break with Claudia Walker was found on the right edge of the box with her snapshot charged down by Bonner.
The killer second came just as the game threatened to open up midway through the second half and in spectacular fashion, Walsh taking a low pass from the right flank and looping an outswinging 25-yard shot that kissed the inside of the post on its way in.
Blues refused to accept defeat, though, and debutant Emma Kelly made an immediate impression, having two shots charged down a minute after coming on with Staniforth’s drive from the loose nicking off Williams and bouncing a fraction wide with Roebuck beaten.
Hampton again impressed by thwarting Demi Stokes with a strong near-post parry late on.
Blues: Hampton, Jordan, Holloway (Harrop 75), H Scott, Mayling, Whipp, Staniforth, Arthur, Grant (Visalli 71), Williams, Walker (Kelly 80).
Unused subs: Brougham, Brooks (g/k).
Man City: Roebuck, Beckie (Stanway h-t), Houghton, Bonner, Stokes, Walsh, J Scott, Weir, Hemp (Wullaert 72), Bremer (Coombs 84), White.
Unused subs: Park, Geum-Min, Fidalgo, Benameur (g/k).
Goals: White 1, Walsh 65.
Referee: Helen Conley.