Morecambe enjoyed the better of the first half and almost took the lead in only the third minute from a free-kick earned after Lee Andrews had hauled down Wayne Curtis.
The Shrimps' top scorer Michael Twiss stepped up and curled a superb effort around the York wall, but saw it come back off the right hand post with Chris Porter well beaten.
The home side continued on the front foot with Darren Kempson heading a dangerous Gary Thompson corner inches over the bar before York keeper Porter reacted sharply to deny Danny Carlton, who threatened to race on to a delightful Twiss throughball.
The visitors struggled to make any headway and were limited to two half-chances in a sterile opening period.
After 19 minutes Clayton Donaldson reacted well to get on the end of Darren Dunning's cross but saw his volley fly wide before the busy Leo Bertos forced the Shrimps' on-loan keeper Steven Drench into a comfortable save.
The hosts then took the lead when Thompson curled a free-kick over the wall and into the bottom right hand corner of Porter's goal.
The pressure continued at the start of the second half with the home side denied a second by an offside flag after David Perkins had rounded substitute keeper David Stockdale.
Five minutes later Kempson was denied a goal when his header from Thompson's dangerous corner beat Stockdale, but was cleared off the line by Jamie Price.
York finally began to find some rhythm after the hour mark. Donaldson, City's biggest threat, dragged a shot wide and Mark Convery missed the target after a gap opened up for him on the edge of the box.
Donaldson felt he was denied a penalty when his chip through hit Michael Howard's arm and the tall striker fired wide again after a quick counter-attack.
But as York pressed, the Shrimps began to find gaps going forward and took full advantage.
Thompson was once again the creator with a storming run down the middle which ended with a pass out wide for substitute Sean O'Connor, who flashed a right-foot drive into the bottom right hand corner of Stockdale's goal.