Southampton's extra energy and purpose surprised Blues in the opening 45 minutes and Swede Mikael Nilsson should have given the home side a deserved advantage at half-time but for wasting a golden opportunity just two minutes before the break.
Fabrice Fernandes, playing in an unfamiliar position behind Blackstock, played a precision pass for Nilsson to race through on goal and round advancing keeper Maik Taylor but he lacked the necessary composure and hit his shot into the side netting.
Delap managed Southampton's first effort on target four minutes after the restart but Blues gradually forced their way into the encounter as Southampton tired.
Manager Steve Bruce was left rueing the lack of a clinical finisher at the final whistle, after watching the Blues miss a series of clear-cut opportunities.
David Dunn forced a good save from Southampton goalkeeper Antti Niemi on 48 minutes after finding space in the penalty area just ten yards out, while defender Mario Melchiot also went close with a 25-yard drive.
Dunn should have done better in the 66th minute when he blasted a shot over when unmarked just 12 yards out, after unselfish play from Emile Heskey on the right.
Darren Anderton, making his full league debut for Blues, thought he had done enough to break the deadlock when finding himself well placed on 76 minutes.
The former England star did everything right as he fired a left footed shot which looked destined for the right hand corner of the net, but Niemi somehow flung himself at full length to brilliantly save down low and Blues were forced to settle for their fifth successive Premiership draw.
In fairness such was the scrappiness of the game neither side deserved three points.