The Premier League side took just six minutes to break the deadlock with Hunt heading home at the near post following Hal Robson-Kanu's ball in from the left and they doubled their advantage through former Blade Mikele Leigertwood in the 40th minute.
Republic of Ireland international Hunt extended their advantage over the League One club early in the second period with a scruffy finish, before Garath McCleary completed the rout in the 54th minute, cutting inside and curling a shot into the far corner of the net.
The opening goal came early on as Robson-Kanu found space on the left flank and whipped in a curling cross which Hunt headed in from eight yards before he embarked upon a celebratory backflip.
Adam Le Fondre, rewarded with a start following his match-winning brace at Newcastle last weekend, burst past three players but George Long came to gather before Hunt could add a second.
United started to briefly come back into the match. The impressive Nick Blackman skipped past his marker and fired a low ball across a packed penalty box, but Adrian Mariappa turned the ball behind.
Reading boss Brian McDermott remained on the edge of his technical area, clearly worried his team had lost the initiative. United's Chris Porter flicked a header just wide of Adam Federici's goal just after the half hour and the Australian did well to save Jamie Murphy's low drive moments later.
Any hopes United had of levelling before the break were dashed in the 40th minute when McCleary found Leigertwood lurking 25 yards out and he unleashed a powerful drive which Long had no chance of stopping.
Reading continued to dominate after the break. Nicky Shorey split the Blades defence with a well-weighted pass, but Long came out to smother before Hunt could shoot.
The seemingly inevitable third goal for the home side came moments later when McCleary cut in from the right and squared to Hunt, whose scuffed shot dribbled past the wrong-footed Long. Reading's fans started chanting "Que sera", clearly convinced the game was over.
And the final nail in the visitors' coffin came after 54 minutes thanks to a great bit of skill from McCleary. The former Nottingham Forest man picked up Le Fondre's pass, and embarrassed his marker with a slalom run into the box before beating Long at his far post.
United almost pulled back a consolation goal on the hour through Kevin McDonald, who saw his drilled shot tipped wide by Federici. The Australian was beaten moments later but, luckily for the Royals, Stephen Kelly was on hand to clear Blackman's shot off the line.
A section of the away support started making their way to the exits. Had they stayed they would have seen Ryan Flynn miss a glorious chance to pull one back, the substitute somehow putting a free header wide from eight yards following a pinpoint cross from Blackman.