Both sides had chances to take maximum points but a mixture of good goalkeeping and poor finishing saw the game end in a blank.
Morecambe went closest to taking the victory when they threatened twice in quick succession midway through the first half. York keeper Nick Pope saved superbly from Padraig Amond's close-range header and Keith Lowe cleared Alex Kenyon's follow up off the line.
At the other end, Shrimpers stopper Barry Roche produced stunning blocks to deny Ryan Jarvis and Lewis Montrose.
The second half saw Stewart Drummond miss three great chances for the home side while at the other end Lanre Oyebanjo failed to get the finishing touch to a dangerous Ben Davies cross.
The York winger was then denied by another superb Roche block before Morecambe ended the game on top with Pope reacting sharply to get down to his left and save a well-struck Jack Sampson shot from the edge of the area, while defender Chris McCready fired wide on the turn when he should have done better.