Team-mate Neil Barrett missed the best chance, blasting over from close range.
Luton could have won it but York keeper Michael Ingham produced a wonderful low diving stop to thwart Rossi Jarvis.
That Ingham save apart, Luton barely threatened and will be the happier of the two sides.
York, protecting an unbeaten home record, created the better opportunities throughout and will feel they missed a glorious chance to strengthen their play-off claims and stretch their lead over the Hatters to seven points.
Michael Rankine, Michael Gash and Barrett, with a fine long-range effort, all went close before the break.
But their best chances before the interval fell to Alex Lawless, who could have had a hat-trick in the space of four minutes.
The best opening of the three saw him cut inside from the left and curl a fine right-foot shot inches away from the top corner.
But the Hatters, battling to continue an amazing league run which has now seen them win six from eight unbeaten games on their travels, could have stolen the points when a 20-yard Jarvis effort forced a splendid save from Ingham.
Left-back Meredith almost grabbed his first York goal with a screaming long-range shot that crashed back off the underside of the bar and was cleared for a corner.
The home side continued to force the pace after the interval and twice the visitors had to scramble the ball clear from near the goalline.
And Barrett somehow contrived to squander the easiest opening of the night, blazing the ball wildly over the bar from eight yards.
Lawless had the final chance but his cross shot was scrambled behind by keeper Mark Tyler.
York: Ingham, Parslow, McGurk, Graham, Meredith, Lawless, Barrett (Purkiss 90), Mackin, Carruthers, Rankine, Gash (Pacquette 73). Subs Not Used: Sangare, Gall, Pitt.
Luton: Tyler, Newton, Kovacs, George Pilkington, Murray, Jarvis, Keane, Nicholls (Blackett 68), Hall (Gnakpa 51), Craddock, Hatch (Barnes-Homer 68). Subs Not Used: Gore, Gallen.
Ref: Billy Khatib (Tyne & Wear).