The highlight of Given's impressive performance was his 55th-minute penalty save from James McFadden.
Scotland international striker McFadden wasted a golden chance to fire Birmingham five points clear of the relegation zone with a weakly taken spot-kick that was palmed away by Given.
To add to Birmingham's frustration they had key midfielder Barry Ferguson sent-off in stoppage time for collecting a second yellow card that will earn him a one-match ban.
It summed up a frustrating game for Birmingham and they will be cursing themselves for squandering a golden chance to beat Mark Hughes' out-of-sorts side.
They had more then enough chances in the first half to pull off an upset but could not find a way past the inspired Given.
Manchester City, who have now drawn their last four Premier League games, still moved into fourth place with a win.
But, without the injured Emmanuel Adebayor, they toiled in attack and rarely carried a threat - the best chance falling to Carlos Tevez who saw his 67th-minute drive tipped over the bar by Maik Taylor.
Birmingham would have been in control of affairs at half-time had it not been for Given.
After Ferguson had shot wide in the seventh minute, Given twice denied Christian Benitez - tipping his first shot on to the post after it had taken a deflection off Vincent Kompany.
Chances for Manchester City were few and far between with Craig Bellamy seeing his shot blocked by Roger Johnson while Shaun Wright-Phillips was frustrated by Taylor.
But it was Given who was by far the busier of the two keepers. He tipped a 27th-minute volley from McFadden over the bar and then plucked a goalbound drive from Lee Bowyer out of their air on the stroke of half-time.
McFadden should then really have made the breakthrough for Birmingham after referee Mike Dean ruled that Nigel De Jong had handled the ball in a challenge with Sebastian Larsson.
Former Everton marksman McFadden tried to stroke the ball low to the left of Given, but the Republic of Ireland international keeper reacted superbly to turn the ball away.