Albion should have had the game wrapped up by half-time only to be undone by poor finishing and goalkeeper Boaz Myhill.
Zoltan Gera ran the show for Albion and he wasted a golden chance to break the deadlock after just three minutes when Myhill beat away his header.
Gera, who also wastefully volleyed over the bar, was also Albion's chief creator setting up both Jonathan Greening and Hartson.
But Greening's header was palmed away by Myhill and Hartson saw his far post header flash wide.
Having spent so long on the defensive, it was ironic that the best two chances of the first half fell to Hull. But they were also undone in front of goal.
Dean Marney, who was making his debut after his £500,000 move from Tottenham, could have made an instant name for himself.
But he stabbed wide from six yards in the 25th minute when he only had goalkeeper Pascal Zuberbuhler to beat.
Substitute Ryan France was equally as well positioned as Marney six minutes before half-time only to head wide.
But the momentum that Hull carried into half-time spurred them on to starting the second period on a high.
Marney, however, wasted another clear chance when his drive was cleared off the line by Curtis Davies after Sam Ricketts cross had hit the post.
Darryl Duffy then somehow managed to lift the ball over the bar from a couple of yards and that was the miss that Hartson really made them pay for.
There appeared to be little danger when Nigel Quashie lifted a throughball forward but Hartson used all his power to bustle past Damien Delaney before lifting the ball over the advancing Myhill.
As Hull pushed forward in the closing stages to try and salvage a point Hartson punished them again, rolling his angled drive under Myhill after another neat pass from Quashie.