The Hornets, who themselves had enjoyed an eight-game unbeaten run prior to the match, looked set to extend that after Darius Henderson had struck twice to seemingly put the home side in control.
However Phil Jagielka started United's comeback a minute after Henderson's second and then a Paul Ifill shot, which deceived keeper Ben Foster, shifted the momentum firmly in the league leaders' favour.
The Blades were then gifted a further boost when Malky Mackay needlessly got himself sent off for kicking out at Rob Kozluk and the visitors surely capitalised on their man advantage to take the points through a Clarke Carlisle own goal.
Watford handed a debut to on-loan West Ham midfielder Carl Fletcher and edged a cagey opening to the game only to suffer a blow when they lost leading scorer Marlon King just 12 minutes in with a hamstring injury.
He was replaced by Henderson, who himself had missed the Hornets' last three games with a thigh strain, but Watford didn't let the setback get to them and gradually began to take a firmer grip on proceedings.
Henderson should have done better when presented with the game's first clear opening after 37 minutes but sliced an Ashley Young cross off target. It then took a fine Jagielka intervention to prevent the former Gillingham man latching on to an incisive Jordan Stewart pass, but from the resulting corner the striker did net his third of the campaign, heading home from close range at the far post after Anthony McNamee' set-piece had cleared Carlisle.
Boosted by the goal, Watford pushed on at the start of the second half and doubled their advantage in the 53rd minute. A long clearance caused indecision between United's centre-halves Chris Morgan and Leigh Bromby and Henderson, sensing his opportunity, won the header and took a touch before calmly beating Paddy Kenny.
But it took United just three minutes to get back into the game when Jagielka directed a header inside Foster's near post following a Kozluk cross from the right.
Watford were partially the architects of their own downfall ten minutes later when a loose Henderson pass was seized upon and the ball worked towards Ifill on the right. The midfielder duly cut inside before unleashing a left-footed shot, the flight of which appeared to deceive Foster as he was wrong-footed.
The home side where now on the back foot and Mackay didn't do them any favours immediately after conceding the second, although his loss of discipline was even less understandable because it occurred in a situation where the Hornets had a promising free-kick opportunity.
But before the set-piece could be taken assistant referee Roger Bone drew Mark Cluttenburg's attention to Mackay's indiscretion and the experienced centre-half was duly dismissed for clashing with Kozluk in the six-yard area.
When the free-kick was eventually taken Kenny tipped over Young's 20-yard effort, but the action was increasingly happening at the other end of the pitch and the Blades scored their decisive third with ten minutes remaining when Carlisle could only turn a Keith Gillespie cross into his own net after the ball had pinged around the Watford penalty area.
The Hornets did muster a late rally but the closest they came to an equaliser was when a Lloyd Doyley long throw fell for Stewart, but he saw his shot deflected over.
Watford were perhaps fortunate not to finish the match with just nine men when Carlisle, then pushed up front as the home side tried to salvage something from the game, escaped with just a booking for a nasty looking challenge on Kozluk.
Man of the Match: Paul Ifill - The summer signing from Millwall did much to fire the Blades to a superb win from two goals behind, netting the equaliser along the way.