The Super League fixture - due to kick-off at 2pm at Halliwell Jones Stadium - was delayed by an hour as Salford awaited results of their latest round of Covid testing.
Unfortunately, two players have tested positive and another two have received inconclusive results meaning they are self-isolating - just five days before their Challenge Cup final against Leeds Rhinos.
In total, Ian Watson’s side - on a five-game winning run - were without a dozen players, given another eight were injured, but the game went ahead to “preserve the integrity of the competition.”
Bottom-placed Rovers were glad they, conversely, ended a five-match losing sequence and dramatically secured only their third Super League win of the year, fittingly as their captain Mose Masoe attended his first live game since suffering his career-ending spinal injury in January,
Pauli Pauli’s high tackle on Matt Parcell saw Ellis hold his nerve with the final kick of the game but there was so much drama before that point.
After conceding a controversial penalty try, Salford thought they were back in contention when Olly Ashall-Bott slipped Jordan Abdull’s tackle for a fine solo effort to make it 18-18.
However, on-loan Wakefield Trinity forward Pauli coughed up possession from the restart and Rovers made him pay.
Weller Hauraki produced a brilliant flick pass out of a double tackle to see Abdull atone for his earlier error, crossing in the 69th minute, but, crucially, Ellis missed the conversion attempt.
He did break clear soon after following a clever Abdull pass but failed to find his support runners.
It meant Salford always had a chance and on-loan London Broncos full-back Ashall-Bolt - who came to life in the final quarter - did wonderfully to slip past Linnett and find Chamberlain who produced a flying finish in the right corner.
Chamberlain could not convert from wide out and it looked like the game would be destined for Golden Point extra-time until Pauli’s late error.
Earlier, Rovers scored first when Kane Linnett made a line break to send supporting full-back Mikey Lewis over in the 18th minute.
Salford responded swiftly when Connor Jones crossed and then Ian Watson’s side showed tremendous defensive resolve to defend four successive sets on their own line.
Short kicks from Ryan Brierely, Elliot Minchella and Jamie Ellis all forced consecutive drop-outs but KR came away with nothing.
Salford had their own chances when Shaun Kenny-Dowall fumbled in Rovers’ 20 and Tony Smith’s side also saw a short drop-out backfire.
But the East Yorkshire club stayed firm and, instead, they went in ahead after Dean Hadley made another break from deep, this time off Jordan Abdull’s excellent flat pass.
Lewis was in support again but Hadley could not find him.
Nevertheless, Rovers moved it wide left on the last tackle where Linnett provided the assist once more with a crisp pass for Ben Crooks to score his ninth try in nine games.
Salford levelled things up when Elliot Kear crabbed across field in the 45th minute and sent Luke Yates crashing through, the prop swatting off Hadley and Linnett to get over from 10m out.
Chamberlain converted as the well-matched contest continues.
Linnett thought he was destined for his second try when he proved too strong again in the 61st minute but Ashall-Bolt got to him and ripped possession clear as the Australian went over the line.
From that drop-out came that controversial penalty try in the 62nd minute.
Ellis threaded a grubber kick through and Lewis rushed through next to the but was pushed in the back by Ashall-Bolt.
Referee James Child had already restarted the game with a 20m tap when he stopped play after receiving a message from his fellow officials saying a penalty try needed to be awarded.
Child returned and awarded the try that Ellis converted. He kicked the all-important one at the death, too.
Hull KR: Lewis; Kenny-Dowall, Abdull, Linnett, Crooks; Ellis, Brierely; Mulhern, Minchella, Maher, Hauraki, Hadley, Garbutt. Substitutes: Parcell, Lawler, Trout, Gee.
Salford Red Devils: Ashall-Bott; Chamberlain, Jones, Kear, Roberts; Gilmore, Atkin; Ikahifio, Ackers, Roberts, Lannon, McCarthy, Burke. Substitutes: Aspey-Davies, Yates, Inu, Pauli.
Referee: James Child (Dewsbury)