Manchester City loan stars James McAtee and Tommy Doyle were both on target for the Blades after Edouard Michut had put the home side ahead.
United bounced back in style after their weekend defeat to Luton, with Boro's draw with Stoke last night giving them the chance to move further clear of Michael Carrick's men in the race for the Premier League.
Here’s how we rated Heckingbottom's men in the game …
9. Sander Berge 7
Survived an early penalty shout when replays showed Batth's header had hit his hand but it would have been incredibly harsh. Enraged the home support again later on by bundling over Batth in the box but again the ref was unmoved. Showed some moments of class but also others when you wish he took command a little more, rather than pass the ball Photo: Simon Bellis
10. James McAtee 8
Had a decent opening to put United ahead inside the first 30 seconds but his shot was blocked. Made amends with a superb piece of composure in the dying moments of the first half, passing calmly into the bottom corner with the type of finish he will have pulled off thousands of times in City's academy. Should have had an assist too but Ndiaye missed the chance. Made way with cramp Photo: Stu Forster
11. Iliman Ndiaye 7
Had a glorious chance to put the Blades ahead after McAtee slipped him clear but Patterson smothered his effort, with a mixture of luck and judgement. Brilliant bit of skill won the free-kick from which Doyle put the Blades ahead before he made way after exerting every ounce of energy he had left Photo: Simon Bellis
12. Daniel Jebbison 7
Came in for his first start since Millwall away and had a good opening early on after Ndiaye and McAtee combined, but his curling effort was palmed away by Patterson before it could find the far corner. Absolutely wiped out by Hume in a tackle that somehow only saw a yellow card before making way for McBurnie Photo: Stu Forster