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  The Red Devils looked down and out as they trailed 18-10 with two minutes left at the Lightstream Stadium.
  But a second try from Niall Evalds and Greg Johnson's score with the last play of normal time levelled the scores.
  O'Brien's missed conversion forced extra-time but he responded with a drop-goal from near halfway to win it.
  It was a dramatic end to an enthralling game and resulted in Hull KR dropping out of Super League after a 10-year spell in the top flight.
  It was also the second time in a week that Hull KR, who did not touch the ball in extra-time, suffered defeat to a late drop-goal.
  Danny Brough's controversial effort last Saturday gave Huddersfield a 23-22 win to condemn the Robins to a place in the Million Pound Game.
  Fighting broke out after the final whistle as Salford fans invaded the pitch to celebrate their side's stunning comeback.
  There was little sign of the drama to come as Hull KR dominated the opening 20 minutes and led 10-0 through tries by Adam Walker and Josh Mantellato.
  Ben Murdoch-Masila touched down from Salford's first real attack and they were remarkably level when Evalds went over in the left corner.
  Mantellato's penalty just before half-time and Thomas Minns' second-half try seemed to have done enough to secure Rovers' place in Super League next season, only to be stunned by Salford's late fightback.
  While Hull KR will play in the Championship next season, Salford's victory means a turbulent year at the AJ Bell Stadium ends on a high.
  They were deducted six points in April for breaching salary cap regulations and had to settle for a place in the Qualifiers after losing their appeal.
  That decision left owner Marwan Koukash considering his future at the club, which he bought in 2013 and has seen finish no higher than 10th.
  But he intimated in the immediate aftermath of the win that he will now stay on.
  Salford coach Ian Watson:
  "Today was glammed up like a Grand Final, but it's a real serious game. I do believe in promotion and relegation, I just don't believe you should play off to decide relegation, you play off to win things.
  "There's a big sense of relief because we felt harshly done to by losing six points. I feel for Hull KR and what they are going to go through in the next couple of weeks.
  "I feel pleased and proud of the boys. It will be a real sense of achievement when they look back.
  "I've seen last-minute drop-goals before but never one like that. It was a massive play by Gaz O'Brien. He's a tremendous kicker of the ball, but I don't think he'll ever kick one like that again."
  Hull KR interim head coach James Webster:
  "Congratulations to Salford, they came up with three really good plays to win the game. They're a team that could strike from distance, we knew that.
  "I'm proud of the boys, they put every single thing into it and that was a real high-quality game. It was one of the better games you'll see this year.
  "The changing room is not a great place to be.
  "I find it hard that a working-class sport can glorify something like this. This game has been glorified as a final. How is it a final? I can't fathom it all. If we'd won, I'd have said the same."
  Hull KR: Cockayne, Sio, Minns, Thornley, Mantellato, Campese, Marsh, Tilse, Lunt, Walker, Blair, Clarkson, Donaldson.
  Replacements: Horne, Peacock, Allgood, Jubb.
  Salford: O'Brien, Johnson, Jones, Sa'u, J. Griffin, Lui, Dobson, Burgess, Tomkins, G. Griffin, Murdoch-Masila, Hauraki, Flanagan.
  Replacements: Kopczak, Krasniqi, Evalds, Kenny.
  Attendance: 6,562
  Referee: Phil Bentham (RFL)
target: Gareth O'Brien kicked a drop-goal in golden-point extra time as Salford won the 'Million Pound Game' 19-18 to relegate Hull KR from Super League.