Dutch striker Emnes raced clear on to Julio Arca's 89th-minute throughball and held his nerve to slide the ball beyond Blades goalkeeper Steve Simonsen for only his third goal of the season to extend Boro's unbeaten run to five matches.
His winner was cruel on United, who had cancelled out Matthew Bates' first-half opener for the visitors through Matthew Lowton before half-time.
Micky Adams' side were chasing the winner when Arca unlocked their defence, but slumped into bottom place as relegation rivals Preston secured a point at Portsmouth, while Scunthorpe upset leaders QPR.
Middlesbrough went ahead in the 18th minute when Bates latched on to Andrew Taylor's cross from the left and drilled a left-footed shot into the bottom corner from 12 yards.
Taylor had earlier lashed a 20-yard shot just wide, but the Blades went close through Lowton, whose angled drive was blocked by visiting midfielder Nicky Bailey.
Boro goalkeeper Paul Smith pulled off a fine save to keep out a close-range effort from Darius Henderson, installed as Blades' skipper, and Bailey then got in the way of Daniel Bogdanovic's goalbound header as the home side chased an early equaliser.
But United midfielder Bjorn Helge Riise stole away down the left channel in the 28th minute and his cross to the far post was headed home by Lowton as the Blades were rewarded for a concerted spell of pressure.
Boro responded through Emnes, but his 25-yard shot was comfortably gathered by Simonsen.
The stopper then denied the visitors with a brilliant save to keep out Scott McDonald's volley from the centre of the penalty area and from the subsequent corner United defender Joe Mattock blocked Rhys Williams' header.
Williams then headed another corner from Tony McMahon over the crossbar and at the other end Henderson directed Riise's cross just wide as both sides went in search of a second goal before the break.
Mattock, on loan from West Brom, forced another smart save from Smith shortly after the restart with an angled drive from inside the area as the Blades dominated possession.
Blades defender Neill Collins headed Quinn's corner off target and Mattock did likewise, before Simonsen kept out McMahon's shot from the edge of the area at the other end.
Simonsen pulled off an even better save soon after, hurling himself full length to tip away Williams' volley, and Henderson headed Riise's cross over the crossbar as the action flowed from one end to the other.
Blades substitute Marcus Bent spurned a gilt-edged chance from Riise's corner on the edge of the six-yard box and Mattock lashed a 20-yard volley wide as the home side launched a desperate late bid for the winner.
But it was Boro who snatched all the points. Substitute midfielder Arca picked out Emnes' run through the middle and the Dutchman kept his composure to tuck his shot inside Simonsen's far post.