© PA Photos
Nick Blackman's second-half penalty was enough to see off cash-strapped Pompey and extend United's unbeaten home league record to 13 games.
Blackman was the only player to register a shot on target in a first half during which both sides were mostly limited to long-range efforts.
The first of his efforts came back off the post, while an ambitious half-volley minutes later went narrowly over the crossbar.
Lively West Bromwich Albion loanee Scott Allan also came close to giving Portsmouth the lead but shot wide following a mazy run.
United applied the pressure after the break as central defender Harry Maguire's turn-and-shot came within inches of opening the scoring.
Blades top-scorer Blackman stepped up to calmly slot past Andersen and earn United the points in front of the biggest League One crowd of the season.