The Blades twice came from behind to win 3-2, Tommy Doyle sealing the victory with an incredible strike in injury time to lift the roof at the Lane.
Manchester City are up next in the semi-final next month as United keep battling on two fronts.
Manager Paul Heckingbottom said: “For us to be in April and be in with a chance of automatic promotion and be in the semi-final of the FA Cup is an unbelievable achievement, it is fantastic and it is a big pat on the back for everyone at the club.
“I’m really focused and intent on us achieving something and not just getting credit, but getting an outcome. It’s been a fantastic season so far and I am focused on capping it off, it could end up being an unbelievable one.
“It could be an unbelievable story, but it’s just a story everyone should enjoy, people should enjoy the position we are in the league and in the FA Cup semi-final. And we will take it game by game now. It’s going to be tight and intense.”
Look through our fans gallery from Sunday’s match at Bramall Lane and see if you can spot anyone you know.
1. Sheffield United fans at FA Cup win over Blackburn Rovers at Bramall Lane
Tommy Doyle of Sheffield United celebrates with teammates after scoring the team's third goal during the Emirates FA Cup Quarter Final match between Sheffield United and Blackburn Rovers at Bramall Lane on March 19, 2023 in Sheffield, England. (Photo by Naomi Baker/Getty Images) Photo: Naomi Baker
2. Sheffield United fans at FA Cup win over Blackburn Rovers at Bramall Lane
A fan arrives outside the stadium prior to the Emirates FA Cup Quarter Final match between Sheffield United and Blackburn Rovers at Bramall Lane on March 19, 2023 in Sheffield, England. (Photo by Jan Kruger/Getty Images) Photo: Jan Kruger
3. Sheffield United fans at FA Cup win over Blackburn Rovers at Bramall Lane
Fans have food and drinks from Sandwich Corner near the ground ahead of the Emirates FA Cup quarter final match at Bramall Lane, Sheffield. Nigel French/PA Wire. Photo: Nigel French
4. Sheffield United fans at FA Cup win over Blackburn Rovers at Bramall Lane
Sheffield United fans arrive at the ground ahead of the Emirates FA Cup quarter final match at Bramall Lane, Sheffield. Nigel French/PA Wire. Photo: Nigel French