The Town were denied by home stopper Michael Ingham in both halves, with Mark Cullen and substitute Luke Rooney both frustrated by fine saves.
Mark Tyler, though, kept the home side at bay with stops to prevent Tom Platt, in the first half, before making an even better save midway through the second half from captain Russell Penn.
Both sides pushed for a winning goal but had to settle for a point at a ground where the Town have now not scored in six matches.
The Town began without skipper Stephen McNulty – beside his girlfriend who was in labour – and his omission was one of two changes that John Still made following Saturday’s 1-0 win against Cheltenham, with Jake Howells and Andy Drury starting in the place of McNulty and Ross Lafayette, who dropped to the bench.
After a slow start it wasn’t until the 11th minute that either side threatened, when the Hatters thought they should have had a penalty when Cullen and Luke Guttridge combined in the box but the handball appeal were waved away by referee Brown.
Back came York, firstly on 14 minutes West Fletcher’s tame shot was easy for Tyler, but four minutes later the Town keeper made an excellent sprawling save to keep out left-back Femi Ilesanmi’s long-range piledriver.
The Hatters then went up the other end and, after engineering an eye-catching move on the break, Alex Lacey should have put the Town ahead. Guttridge’s left-wing corner was half-cleared but the midfielder’s second cross was perfect for Lacey at the back-post only for the young centre-half to head wide with the goal gaping.
As the half wore on the Hatters were finding their rhythm with a series of fine passing moves, and on 25 minutes one such attack almost saw Cullen break the deadlock. Saturday’s match-winner raced clear down the left side but after haring into the box he saw his shot somehow saved by the fingertips of home stopper Ingham.
Having rued not taking their chances in previous games this season, the Hatters did not want to concede a goal given their dominance with the ball. However, Tom Platt headed wide on 30 minutes before Tyler again came to the Town’s rescue a minute later when parrying Lindon Meikle’s goal-bound effort.
As the game continued to swing from end to end, a dozy York defence almost allowed Cullen a chance into box before Ingham then fumbled a low Scott Griffiths cross second later only for the loose ball to evade a man in white.
Cullen and Guttridge linked-up well on 40 minutes but failed to create a clear-cut chance before Tyler then made his third good save of the first 45 minutes when quickly down to deny Platt’s low shot with his legs after Russell Penn’s pass.
After the break it was the Minstermen who started the brighter; Luke Summerfield drilled a low shot wide three minutes after the restared before Fletcher whacked a shot from the edge of the box way over the crossbar.
On 52 minutes the Town made their first change, introducing Rooney for an injured Jake Howells and seconds after the substitution, Lacey headed over following a right-wing corner.
The chances continued to come for the Hatters with a razor-sharp run from Pelly Ruddock Mpanzu on 58 minutes ending in the midfielder’s shot saved by the legs of Ingham. A minute later Rooney then fired a shot into the arms of the York goalkeeper from the edge of the penalty as the Town upped the ante.
But back came the Minstermen and Tyler again was to the rescue when it seemed all the world that Penn would tuck home Michael Coulson’s pass when free 10 yards out. It was a magnificent save and it helped see out a spell of heavy pressure from the home side.
And the Town came closer themselves on 73 minutes when Rooney was denied by a breathtaking save by Ingham, who somehow tipped over the substitute’s drive after he had danced past the challenge of two York men.
The game continued to flow from one end to the other and a hooked shot from Cullen with 15 minutes left was kept out by Ingham, surprised at his near post.
As time ticked down Rooney then tip-toed through the York backline to force Ingham into a diving stop before Guttridge’s pass almost picked out Drury at the back post.
Both sides desperately searched for a late winner in the dying stages but in the end the deadlock could not be broken as both sides had to be content with a point.
TOWN: Tyler; Williams, Griffiths, Lacey, Wilkinson; Howells (sub Rooney 52), Ruddock Mpanzu, Drury, Smith (sub Stevenson 62); Guttridge, Cullen (sub Lafayette 82). Subs: Wall, Whalley, Connolly, Justham.
ATTENDANCE: 3,649, including 445 supporting the Town.