Portsmouth had a chance inside the first minute as Tommy Smith pounced on a missed header from defender Anthony Gardner, but after running in clear on goal the ex-Watford man dragged his effort wide from 12 yards.
Geovanni came close from a free-kick moments later, but his right-foot effort from 20 yards curled over the visitors' crossbar.
Hull came close from another free-kick on the ten minute mark, as Stephen Hunt whipped in a left-footed cross from the right which seemed to evade any touch as it skimmed across six-yard box and into the welcome arms of keeper David James.
Dean Marney then tried his luck for the home side, but his right-footed shot from 20 yards flew just over the Portsmouth cross-bar.
Smith was presented a chance towards the end of the first half as Dindane found him with space inside the box, but the Pompey striker failed to connect with his shot, allowing the Hull defence to clear.
Portsmouth had a great chance on the hour mark as a free-kick on the right from Jamie O'Hara saw the ball land at the feet of Dindane, but the Lens loanee could only fire his close-range effort straight at keeper Boaz Myhill who did well to palm the strike away.
Paul Hart's men came close again moments later, as Kevin-Prince Boateng whipped in a cross from the right which saw the ball take an awkward bounce in front of keeper Myhill, but the Hull number one managed to dive to his left and turn the ball away for a corner.
O'Hara came close from a free-kick with minutes left after Myhill had spilled the ball and brought down Dindane just outside the box, but the ex-Tottenham midfielder saw his curling left-footed effort flash just wide of the post.