They had the edge over Stranraer throughout but had to settle for a share of the points which suited the home side much better.
The first half was one to forget apart from the 35th minute which meant a lot to the few City fans when their side - clearly the better outfit in the opening period - grabbed the all-important opening goal.
It came from the head of Gerry Britton who nodded the ball into the net from a Stuart Callaghan corner and Britton certainly deserved the score.
He had put himself about, popping up in the open spaces and always offering a target for a team-mate with the ball.
But, despite their superiority, City showed why their league position is so lowly as, their goal apart, they failed to make an impact when they got among the home defence.
Stranraer were no better, registering only a couple of chances which went wide and showing up poorly when it came to passing and teamwork.
Yet it was Stranraer who scored next, levelling in the 73rd minute through David Hamilton.
The midfielder rose to meet Ian Ross' corner and steered a header downwards past stranded keeper Craig Nelson.
And it was Nelson who stayed in the limelight for all the wrong reasons as this game ended in a draw.
Two minutes into injury time he sprinted out of his penalty area and handed Allan Jenkins' shot.
For his troubles Nelson was shown a straight red card and substitute keeper John Hillcoat had to leave the bench for the final few seconds.