Lee Hills had volleyed them ahead just after the hour and Julian Speroni had saved a penalty in the frenzied climax to a game which took time to come alive.
McCombe's saver for City came right at the end of an extra four minutes and there was barely time for a restart before the final whistle.
Speroni's spot-kick parry from Bradley Orr's penalty was followed by an even better save as Orr swooped on the rebound, but the final minutes were all played out around the visitors' goal area.
Neil Warnock had made four changes in a bid to end Palace's poor run but they have now taken only two points from 15.
A power cut set back the start by 15 minutes and tactically much of the football from both sides in the first half was in the dark.
The Eagles made a bright start, but faded before the eager, hard-working City thrust forward, but the home side suffered by using Dele Adebola as their only striker.
With Speroni reading the crosses well Palace were seldom under real pressure, but had a moment of panic when Matt Lawrence obstructed Adebola's run on goal.
Fearing a red card they swarmed around referee Roger Beeby, but he had made up his mind the striker had not got through to a scoring position and that a yellow would suffice.
Palace made their physical presence known in the second half and Mark Hudson went close to giving them the lead with a header, before Hills produced a superb strike from Ben Watson's squared pass.