Having performed well in the first half, Pompey sat back in the second half and allowed United to dominate possession and press hard for an equaliser, which to the relief of the home fans, didn't arrive.
Joel Ward came back into the side at Kanu's expense but that may have been too soon as the youngster seemed to be lethargic, but that didn't stop the other players playing some good football in the first half.
The passing was quick and everyone seemed to know where everyone else was going to be. Micky Adams' men struggled to cope with Cotterill and Nugent and it was the latter who won the corner that led to the goal thanks to some neat trickery and a testing shot for Steve Simonsen to save.
David Cotterill whipped in the corner kick which the United defence struggled to clear and so Hermann Hreidarsson bundled the ball home from close range.
The Blades did have a chance to equalise in the first half through Richard Cresswell when his shot was saved by Ashdown but the Blues should have extended their lead late in the half when Kitson squared the ball across goal but Hreidarsson's diving header sent the ball narrowly wide.
Pompey had a great chance to double the lead right after the break as Simonsen spilled Kitson's shot but Nugent could only hit the rebound into the side netting.
That was as good as it got for the home crowd as Sheffield United turned up the heat and began to dominate possession without forcing Ashdown into a meaningful save.
However, Stephen Quinn should have equalised when he was found free in the box with space to shoot but he fired wide of the far post.
The crowd frustrations continued as Pompey really struggled to keep hold of the ball as nervous clearances led to mounting pressure from Sheffield United who kept plugging away but were being denied by last ditch blocks or the ball being hoofed away in panic.
Sam Vokes had a late chance but his header was straight at Ashdown and Pompey wasted an opportunity in stoppage time to be absolutely certain of the result when Simonsen was caught well out of position but Nugent again fired into the side netting when he should have squared the ball for a player to fire into an unguarded net.
In the end, a single goal was enough to seal a sixth straight win without conceding for Steve Cotterill's men, equalling a record set in 1979.
On balance of play, it was hard to argue that we were deserved winners but I suppose this result could be considered karma when Pompey were beaten by a soft, deflected free kick at Bramall Lane having been the better side.
It was strange to see a good first half performance followed by a poor second half as it's usually the reverse. Perhaps the players are feeling fatigued as it's virtually the same eleven who have had to play so many games in a short space of time?
If it is that, then that's not good news as there is little time to recoup before Tuesday's trip to Ashton Gate to play a Bristol City side who have found some form.
That's not to say we should worry too much, either, as no team in the country is in better form than Pompey right now. It's just a question of how long this run can be sustained.
Making hard work of beating the worst teams in this league might be a concern for the future but, who knows? If we can keep this superb run going then perhaps a late surge towards the play-offs isn't such a ridiculous idea after all?
Pompey Player Ratings
Jamie Ashdown: 6 - Made some comfortable saves.
Ritchie De Laet: 6 - Runs were restricted, barring one surge that almost led to a goal.
Ricardo Rocha: 8 - Always there to sniff out the danger once again.
Greg Halford: 6 - Looked a bit nervous, especially late on.
Hermann Hreidarsson: 8 - Did well defensively and bagged the crucial goal.
Jonathan Hogg: 6 - Worked hard.
Hayden Mullins: 7 - Linked play well.
David Cotterill: 6 - Faded in the second half.
Joel Ward: 5 - Seemed jaded, perhaps not fully recovered from injury.
David Nugent: 6 - Probably should have scored, but caused problems in the first half.
Dave Kitson: 6 - Worked hard and took some undeserved stick when he was isolated up front.
Substitutes
Darryl Flahavan
Carl Dickinson (Cotterill 80): N/A - Brought on to hold the lead.
Aaron Mokoena (Hogg 71): N/A - Slotted in fine.
Tom Kilbey
Nadir Ciftci
Kanu (Ward 71): N/A - Impact not as great as in previous games.