Hart belied his tender age to pull off a number of key saves to deny Pompey, who themselves were gunning for a top-four place.
The England Under-21 international caught the eye in a game full of quality and chances, but one which couldn't find a goal to match the excitement.
Portsmouth boss Harry Redknapp recalled fit again Nwankwo Kanu to his starting line-in in place of the suspended Papa Bouba Diop and the Nigeria international was back to his eloquent best inside the first minute as he shrugged off the attentions of Richard Dunne to shoot goalwards only to be denied at the near post by Hart.
Pompey continued to take their good form from last week's 4-1 win at Newcastle and were unlucky not to take the lead on 20 minutes when Sulley Muntari and Kanu combined to play Niko Kranjcar in only for Dunne to make a crucial last-ditch tackle to deny the Croatian.
The pressure was beginning to mount on a City side whose last away performance was the 6-0 drubbing at Chelsea.
But they had 20-year-old Hart to thank as Glen Johnson turned inside Dunn onto his left foot, leaving the goal at his mercy.
Somehow though, Hart got the faintest of touches to divert the ball onto the crossbar.
City continued to be busy at the back and their best source of a goal looked on the counter attack.
That almost rang true when, five minutes before the break, Elano played in Darius Vassell down the right-hand side.
The City striker managed to pick out Martin Petrov in space, but fortunately for Pompey the Bulgarian hit his shot straight at David James.
With the game finely balanced in the second half, Vassell was then guilty of the miss of the game as Petrov crossed on 50 minutes leaving the England international the easiest of opportunities, but he lost his footing and skewed embarrassingly wide.
David Nugent was introduced with 30 minutes to go and the almost forgotten £6million man went agonisingly close minutes after his introduction with a blockbusting strike from distance which took the slightest of deflections and came back off the inside of the post.
A draw was undoubtedly the right result in a game between two teams full of quality but whose strengths ultimately lie in their respective defences.