The Blades twice trailed to Rovers but came back twice before Tommy Doyle scored a screamer of a winner to book United’s place at Wembley in the dying minutes of the game.
Here’s how we rated United’s players on an afternoon to remember ...
9. Sander Berge 7.5
A rather typical Berge performance in many ways - some very promising moments and some frustrating ones. The way he shifted his weight and glided past Szmodics like he simply wasn't there earlier in the game showed what can be done but he couldn't grab the game by the scruff of the neck until late on when his calmness on the ball helped United as they looked to get back into the game Photo: Andrew Yates
10. James McAtee 6
Enjoyed a superb early chance to give United a dream start when Egan's excellent pass sent him clear, but his finish lacked a bit of conviction and looked a nice height for Pears to palm it away. Had a good opening seconds in the second half as well after a good United move but he seemed to be stuck between hitting and controlling it and in the end did neither, before having another glorious one-on-one chance saved by Pears Photo: Simon Bellis
11. Iliman Ndiaye 8
Could control a high ball and fend off his opponent in a phonebox, often frustrating Blackburn's defenders with his strength and skill as they harried and harassed him. Unfortunately United couldn't get him in areas high enough to really maximise that threat as often as United would have liked but another eye-catching display from the Senegal star, who is destined for the very top Photo: Andrew Yates
12. Oli McBurnie 8
Cut a forlorn figure for much of this game as he struggled to link up effectively with strike partner Ndiaye. An ever-willing runner in behind but snatched at a chance with just over 10 minutes to go and hit the stanchion rather than the target on his left foot. But kept going, to his credit, and a great bit of skill and tenacity saw him drag United back on level terms again Photo: Andrew Yates