Looking to bounce back from the midweek defeat to promotion rivals Middlesbrough, United twice levelled but were left heartbroken late on as Bradshaw pounced from close range to seal victory for his side.
Here’s how we rated the Blades on a disappointing evening in the capital ...
9. Tommy Doyle 6
Back in the side after his recent absence with a calf issue and made his mark with a free-kick to drag the Blades level at the break. Looked to build on that in the second half but then made way 10 minutes into it, being replaced by Ben Osborn - hopefully not because of a fitness issue Photo: Andrew Redington
10. Sander Berge 4
May have been a touch fortunate to see out the game after going down very easily in the first half in a forlorn effort to win a penalty and then getting booked later in the half for dragging back his man in midfield. Some nice moments but some really frustrating ones too Photo: Paul Terry
11. Daniel Jebbison 4.5
Returned to the scene of his FA Cup strike last month at Iliman Ndiaye's expense, Jebbison was left chasing lost causes for most of the first half but did win the free-kick from which United dragged themselves level. Almost put United ahead but his shot was well-saved by Long Photo: Paul Terry
12. Oli McBurnie 4.5
His partnership with Jebbison didn't fire in the first half but almost lit up the second when his lovely ball sent his partner through, but Long did well to block. Booked in the second half after being adjudged to have left a foot in on a Millwall defender as they chased a throughball Photo: Paul Terry