Despite knowing that a win would move them back into the top four, the Rhinos were comprehensively outplayed by the Robins, who followed up their 17-10 win at Headingley Carnegie in March with another victory.
The result means that Leeds have now lost eight games this season – two more than they did during the whole of 2009 – and that the current occupants of fourth place, Hull, could be three points clear of them by the end of the weekend.
They were also dealt further blows on the fitness front, with Rob Burrow, back after two months out with a knee injury, limping off, and Lee Smith joining him on the sidelines.
None of that will be of any concern to Rovers coach Justin Morgan, though, who still harbours hopes of a top-four finish for his own side.
He watched on as his men scored three first-half tries and one late on, but more importantly, thanks to props Joel Clinton and Mick Vella, bullied the champions into submission, meaning Ryan Hall's try was little more than a token effort.
Leeds, who were expected to welcome three players back from injury but only selected Burrow, had two early opportunities to score.
The first saw Carl Ablett ankle-tapped by Rovers debutant Josh Charnley as he shaped to run the length of the field, before video referee James Child deemed that Danny McGuire had committed a double movement as he crossed off Ablett's ball.
That proved to be the catalyst for Rovers to fire into life.
They took the lead in the seventh minute as Ben Galea stepped his way past Smith for a fifth try of the season and, although Ryan Bailey should have levelled for Leeds when he shelled the ball on the line, it did not stop Rovers doubling their advantage through Ben Fisher's 18th-minute dart.
Childs then denied Leeds again, deciding that Ablett had not reached the line after a scrappy off-the-cuff move, before Peter Fox picked up Burrow's errant pass to race 60 metres to the post two minutes before the interval.
In-form winger Fox, aiming to reclaim his England spot at the end of the season, would have had a second try in the 49th minute had Charnley sent him in at the corner rather than going it alone after Clint Newton's offload.
Charnley's naivety looked a potentially costly error two minutes later as Leeds opened their account through Hall's fourth try in as many games – the winger having plenty of time to ground Burrow's kick through.
Smith limped out of the action with 25 minutes remaining to pose Leeds a further problem in their bid to overturn the deficit, but that task would have been all the easier were it not for Fox's stunning last-ditch tackle to stop McGuire as he raced onto Jamie Peacock's offload.
Scott Murrell made a hash of a drop-goal attempt as Rovers looked to close the game out, before Michael Dobson succeeded in putting 13 points of distance between the two sides with 12 minutes left.
Hall looked set to bring Leeds back into it again after Burrow gave him a free run to the line, but he dropped the ball, summing up his side's night, and things were soon made worse for Hall as Ben Cockayne slid over at the other end.
Burrow then limped off the field to complete a miserable night for Leeds.
Hull KR: Briscoe, Fox, Charnley, Cockayne, Latus, Murrell, Dobson, Vella, Fisher, Clinton, Newton, Galea, Watts. Substitutes: Hodgson, Cook, Netherton, Lovegrove.
Leeds: Smith, Donald, Delaney, Senior, Hall, Sinfield, McGuire, Bailey, McShane, Peacock, Ablett, Jones-Buchanan, Clarkson. Substitutes: Burrow, Kirke, Ambler, Pitts.
Referee: T Alibert (Toulouse).
The Rugby Football League have appointed Bev Risman as their new president.
The 72-year-old, who was a capped fly-half for the England and British Lions rugby union sides, also won five caps for Great Britain in league.
Wigan Warriors went six points clear at the top of Super League after beating Salford 60-10, while St Helens slumped 30-20 against Catalans Dragons.