The goals came early in each half, but the visitors were giving a helping hand on each occasion at the KCOM Stadium.
Jacob Greaves appeared to send the first into the net under pressure from Sean Raggett, while Josh Magennis then did the honours after the break.
Kenny Jackett made one change from the side that drew with Fleetwood on home soil earlier in the week.
Jack Whatmough was feeling ill on the morning of the match, so his place in the centre of defence was taken by Rasmus Nicolaisen.
The visitors made a bright start and Marcus Harness’ effort was deflected behind after the winger had swapped passes with John Marquis.
And the deadlock was then broken from the resulting corner, although Hull were upset that the goal was allowed to stand.
Raggett tried to attack the delivery Cam Pring, but GREAVES stooped to try to clear and ended up heading the ball into his own net.
He complained of a boot to the head from the Pompey centre-back, although referee Michael Salisbury disagreed.
The Tigers tried to hit back immediately and when Josh Emmanuel cut the ball back into the box, Mallik Wilks slotted wastefully wide.
It was Pompey looking the more dangerous side, though, and Ryan Williams – who featured in the Blues’ last visit to the KCOM Stadium in 2011 – saw a shot diverted past the post.
Josh Magennis then did well to head clear another Pring corner, as Nicolaisen came charging in to try to meet it himself.
But the hosts grew into the contest and began to threaten themselves, with a James Scott cross drifting towards the net and having to be tipped over by Craig MacGillivray.
And Pompey also had to deal with a series of corners towards the end of the half, but defended resolutely to go in ahead at the break.
Hull City 0
The visitors had to survive a scramble in their box straight after the restart, with Hull unable to take advantage of several mis-kicks.
It was a similar story just a few seconds later, although this time Pring was well-placed to hack the ball clear.
But Pompey shook off that shaky opening to the second period and soon managed to double their advantage.
Once again, however, it appeared to be another Tigers player who gained the unwanted credit for the ball crossing the line.
A Ronan Curtis free-kick was nodded on by Nicolaisen towards Marquis, but MAGENNIS got there first and sent the ball past Matt Ingram and into his own net.
MacGillivray stopped an instant reply from the hosts, beating away a fiercely-struck fizzer from Regan Slater.
Pompey were looking pretty comfortable, although Mallik Wilks could not connect with a teasing Keane Lewis-Potter delivery at the back post.
But the Tigers finally roared into life in the closing stages, with a couple of dangerous crosses causing problems.
Greg Docherty then lifted a pass into the box and it looked like Magennis had reduced the deficit, only for his header to come back off the bar, with Nicolaisen doing the mopping up.
There were to be no more scares, however, as the Blues saw out the final few minutes to leapfrog their opponents at the summit.
Hull (4-2-3-1): Ingram; Emmanuel, Burke, Greaves, Elder; Smallwood (c), Docherty; Wilks, Slater (Eaves 62), Scott (Lewis-Potter 46); Magennis
Subs not used: Long, Coyle, McLoughlin, Batty, Adelakun
Pompey (4-2-3-1): MacGillivray; Johnson, Raggett, Nicolaisen, Pring; Naylor (c), Cannon; Harness (Jacobs 88), Williams (Close 87), Curtis; Marquis
Goals: Greaves 6 (og), Magennis 55 (og)
Subs not used: Bass, Mnoga, Morris, Hiwula, Harrison
Referee: Michael Salisbury