And, just like he did against Gateshead the previous week, James Armson grabbed the crucial goal.
It came on 27 minutes when Glenn Walker’s corner found Armson unmarked and his header beat Pete Jameson in the York goal.
Shep Murombedzi’s low shot was kept out by the keeper’s legs before York produced a moment of danger late in the half as Lenell John-Lewis reached the by-line, bringing a double save from Danny Lewis.
The Minstermen’s defence allowed a carbon copy opportunity for Saints to double the lead as another corner picked out Connor Franklin in space but this time Jameson saved.
Murombedzi saw his fierce effort well saved at the near post before Jaanai Gordon’s effort brought a terrific one-handed stop.
Armson was close to repeating his opening goal as he won the aerial battle only to head narrowly over.
York enjoyed periods of possession without creating clear cut chances but the Brackley defence had to be on their mettle to defend the lead.
The closest the visitors came to an equaliser was from Scott Barrow’s fine cross that just evaded an attacking head late on.
The win means Brackley made it 17 games without defeat and remain a point clear of Gateshead with both teams having six to play.
Boss Wilkin said: “It was a big win for us against a good team.
“We knew it would be a really tough game for us and we’d need to be focused and concentrated.
“Fortunately we’ve come through with the three points.
“It’s a well worked corner, the ball is in the air for a long time and to guide the ball in the way he (Armson) did is a fantastic skill. It gave us that platform from which to try to build.
“We had to make some enforced changes but the players off the bench have acquitted themselves well.”
Brackley travel to Leamington on Good Friday (3pm) while Gateshead head to Guiseley.