Jake Heatley had put Town ahead after ten minutes with a well placed header, but Knaresborough hit back almost immidietely from the start of the second half, before Baird claimed what turned out to be the winning goal five minutes later.
The first action of the evening say Louie Gibson's right wing cross headed back across goal and in by Jake Heatley.
Andy Higgins nearly made it two in the 22nd minute as the central defender headed a corner towards goal, but saw his attempt cleared off the line.
The visitors finished the half strongly, but didn't get the elusive equaliser, until inside the first minute of the first half when Town were slow coming out after the interval.
The sides were only level for five minutes though, as Baird rattled a free kick in off the post!
Town should have had a third soon after when the ball broke to Prince Attakorah with the goal at his mercy, but the winger could only find Baird's legs and Knaresborough escaped.
Attakorah went close again with a bending shot in the closing stages, though the score stayed at 2-1 as Town continued their winning streak.
Town U21s: Powell, Swain, Gibson, Dolby, Higgins, Brettel, Attakorah, Barker, Baird, Clark, Heatley
Subs not used: Steele, Webster, Phoenix, Smith
Goals: Heatley 10, Baird 51