Chris Wilder’s side hold a 3-0 lead heading into the second leg of the semi-final tie at Bramall Lane, and will be confident of now booking their place at Wembley with minimal drama.
It was a nightmare night on home soil for Bristol City, who had Robert Dickie sent off late in the first-half and then conceded three goals to leave them needing a miracle.
Sheffield United finished third in the Championship this season with 90 points and were therefore the favourites to come through the play-offs, despite their miserable record.
The Blades have been involved in the play-offs nine times in either the Championship or League One, and have failed to secure promotion on each occasion.
They will be hoping that changes here, with either Coventry or Sunderland waiting at Wembley for whoever comes through this tie.
How to watch Sheffield United vs Bristol City
TV channel: In the UK, the game will be televised live on Sky Sports. Coverage begins on Sky Sports Football and Sky Sports Main Event at 7pm BST, ahead of kick-off at 8pm.
Live stream: Fans can catch the contest live online via the Sky Go app.