The home side came out the blocks firing but their best chance of the first half came to Steven Davies, who swerved the ball towards the far post only for Miguel Llera to make a crucial interception to keep the scoreline level.
City were eventually punished by Jermaine Johnson, who found the back of the net from a shot inside the penalty box, which slid into the bottom right corner.
The visitors came out in the second half overpowering the home team, but City tried to get back into the game through Marvin Elliott.
The City player produced a right-footed shot from outside the penalty box, but his effort was driven out wide.
The struggling Championship outfit may have felt hard done by when they were denied a penalty by the referee towards the closing stages of the second half.
Greg Cunningham looked to be brought down inside the area, sparking calls for a penalty, but instead, the match official booked him for diving.
An unlikely equaliser eventually came for the home side due to a mistake from goalkeeper Chris Kirkland, who spilled a cross that allowed Baldock to latch onto the end of it and fire into the back of the net.