After a scrappy start by both teams, Pompey took the lead after 21 minutes. Patrick Agyemang sent over a looping cross following good work by Jed Wallace on the right-wing and Shaun Cooper headed powerfully into the bottom left corner of the net.
The home side, whose fans completed a buy-out of the club on Friday night, doubled their lead just three minutes later when Wallace fired a low ball into the six-yard box which David Connolly poked home from point-blank range.
And just after the half-hour Wallace got his name on the score sheet, side-footing home from eight yards out after a fine left-wing run and cross from Connolly.
The Blades, who confirmed their place in the League One play-offs but saw their hopes for automatic promotion end with the defeat, offered little going forward and looked disorganised in defence.
A disallowed Chris Porter header on the stroke of half-time was the closest they came to breaching the Pompey defence.