Darlington dominated the opening half and new striker Billy Clarke was denied on three occasions by City keeper Paul Jones.
In the 11th minute a left-foot drive from Clarke was saved by Jones and on the half-hour mark the keeper parried a shot from the edge of the area and then four minutes later the keeper was well placed to deny Clarke yet again.
In the opening minutes of the game Darlo had struck the woodwork and so after dominating the half, it was no surprise when they took the lead five minutes from the interval and again Clarke was involved.
City defender George Friend brought down the on-loan Ipswich man and the penalty kick was despatched low past Jones by Rob Purdie.
Former Ipswich striker Marcus Stewart should have equalised seconds from the interval, but he put his unmarked header wide.
In the second half the Darlington keeper Simon Brown denied Rob Edwards just three minutes after the restart and then on 54 minutes another header from Stewart was saved by an acrobatic save from the home keeper.
As the game reached the hour mark defender Dan Seabourne became the player to score City's first goal back in the league when he headed in at the far post to convert a free-kick from Edwards, after Darlington midfielder Ricky Ravenhill had brought down Friend.
Darlington had to make three quick changes. Ravenhill was replaced by Robin Hulbert in the 69th minute at the same time that Adam Proudlock was replaced by Gregg Blundell and then two minutes later Neil Austin replaced defender Clayton Fortune, who had picked up a shoulder injury.
In time added on at the end Darlington midfielder Jason Kennedy could have grabbed all three points with a shot from the edge of the area that went narrowly wide.