Leading scorer Richard Brodie, who should have had a hat-trick, was the chief culprit and to complete an unfortunate day he also picked up his 12th caution of the season, this time for diving.
He headed over from close range in the first half and then failed to beat Stuart Coburn after being sent clear by Ben Purkiss after the interval. Finally, with five minutes to go, he had a remarkable miss when standing virtually underneath the bar, he somehow shot over.
Manager Martin Foyle reverted to a 4-4-2 formation after adopting 4-3-3 in the midweek defeat by Salisbury and there was a clear improvement with Adam Smith sparkling on the right wing and Courtney Pitt crossing some dangerous centres from the left.
The defence, guilty of crucial errors in the recent bad spell, looked strong and goalkeeper Michael Ingham has seldom, if ever, had an easier afternoon.
The second half saw York attack continuously and if they can maintain this flowing football – and improve their finishing – they should maintain their promotion hopes.
Foyle said: "We played some exceptional football and created a lot of changes.
"It was a heartening performance from the lads with a lot of good things to see after our poor run."
Altrincham: Coburn; Densmore, Young, Williams, Brown; Denham (Corden 65), Danylyk, Doran, Clee (Welch 78); Little (Moyo-Modise 57), Senior. Unused Substitutes: Saunders, McAliskey.
York City: Ingham; Purkiss, Graham, Sangare, Meredith; Smith, Mackin (Harsley 65), Clarke, Pitt; Brodie, Gash (Rankine 68). Unused Substitutes: Gall, Pacquette, Parslow.
Referee: J Simpson (Carnforth)
Man of the Match: Adam Smith.
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