The visitors rarely threatened as an attacking force, but held the home strike force well, with centre backs Michael Nelson and Christ Westwood outstanding.
It was a game of few clear chances and the only two of the first half fell to City.
Paul Heffernan's 20th minute shot was blocked by Nelson after he had been set up by Mickey Bell's break from the left flank.
Ten minutes later Bell switched to the right to deliver an in-swinging free-kick which was flicked on by Danny Coles only for Westwood to lunge in and clear the ball off the line.
Hartlepool boss Neale Cooper reacted to his side's lack of threat by substituting strikers Adam Boyd and Joel Porter at half time.
It made little difference as the only effort of note for home goalkeeper Steve Phillips to deal with was a 76th minute chip from 25 yards by Mark Tinkler, which he comfortably pushed over the bar.
City player-manager Brian Tinnion also made three second half changes. He sent on first Scott Murray and later Lee Miller and 17-year old Dave Cotterill in a bid to pep up his attack.
Top scorer Leroy Lita headed just over on 52 minutes, but despite some heavy late pressure City lacked the invention to unlock a strong and well organised Hartlepool rearguard.
It was frustrating Christmas fayre for a crowd of over 13,000. The final whistle was greeted by jeers from the home supporters as City continue to fail to justify their pre-season tag as promotion favourites.