Things went wrong in the 53rd minute though when Boaz Myhill gave away a penalty and was sent off. Matt Duke came off the bench but couldn't keep out Gavin Strachan's penalty.
Alan Pouton then levelled on the hour mark and 10-man City were up against it.
Neither side were able to score again before the 90 minutes were up, so the match went into extra time. Substitute Stuart Elliott made it 3-2 to City with a deflected shot 2 minutes into the second half of extra time, but Joel Porter's equaliser sent the game to penalties.
Stuart Green was the only Tiger to convert his penalty, with Stuart Elliott and Ian Ashbee both denied. Pools managed to score all four of theirs to send them into the 2nd Round.