Rovers played for nearly 20 minutes of the second half with only 12 men and were briefly down to 11 after yellow cards for forwards Albert Vete and George Lawler.
Trailing 24-10 after 45 minutes Leigh, now winless in 15 games, staged a thrilling comeback to lead 28-24.
But Shaun Kenny-Dowall’s second try of an exciting spectacle and Hall’s latest touchdown to extend his lead as the competition’s top try-scorer ensured Rovers went above rivals Hull FC to fifth in the table on win percentage.
Even then Leigh skipper Liam Hood then had a potentially equalising try disallowed for offside.
Leigh made a turbo-charged start, as Junior Sa’u finished a flowing move after just 58 seconds before Joe Mellor had a ‘try ruled out by video referee Liam Moore.
But Leigh could not sustain their momentum, young half-backs Rowan Milnes and Mikey Lewis at the heart of a Rovers revival that brought 14 points in seven minutes.
Kane Linnett and Greg Minikin profited from intervention by Milnes, the youngster’s second angled kick plucked out of the air by Brad Takairangi for his winger to run round the short side and touch down.
Then it was Lewis’s turn, providing the pass assist for Kenny-Dowall’s 23rd-minute try before showing and going himself for a 34th minute try to make it 18-4.
A try by Craig Mullen which he also converted dragged Leigh back into contention but Vete’s beefy barge over, goaled by Crooks, restored Rovers’ 14 point cushion.
That lead though quickly evaporated as Tongan giant Vete and Lawler were sin-binned. Leigh made the two-man advantage tell when Sa’u dashed in for a second try. And though Vete returned, Lewis was forced off with a head injury.
With Rovers still down to 12, Sidlow’s second try put Leigh back in front at 28-24.
Kiwi ace Kenny-Dowall tied the scores with his own second try after 67 minutes before Hall went over late on to seal a stunning win.
Tony Smith believes KR’s dramatic late comeback win will stand his side in good stead for the rest of the Super League campaign.
“There was some ugly rugby league, a lack of control by both teams,” said head coach Smith. “It was a bit helter skelter.
“But you have those days. Going down to 11 men was enormous and tests most teams’ resolve.
‘The other thing we haven’t had to do too much of in the past is come from behind to win games. It is something we need to do.
“It wasn’t planned that way and I didn’t set it up on purpose that way. It wasn’t part of our tactics to go behind.
“But it will do us good. It was great experience. And we were up against a dangerous team.
“So, I am not going to be too hard on the players. They are working hard for each other and there is great spirit in the camp.
“The effort was there but we were lacking in smarts at times.
“I was completely relaxed about it,” insisted Smith over Leigh’s bid to end their losing streak. “If we had lost, we would have lost.
“So, I wasn’t getting into too much of a panic. As I get older, I might get a bit more like that. I am just willing to accept whatever the result is.”
Leigh: Brand, Russell, Thornley, Logan, Sa’u, Mellor, Mullen, Bell, Hellewell, Foster, Sidlow, Eaves, Gerrard. Substitutes: Hood, Thompson, Gee, Ioane.
Hull K R: Crooks, Minikin, Takairangi, Kenny-Dowall, Hall, Lewis, Milnes, Sims, Hadley, Linnett, Maher, Parcell, King. Substitutes: Vete, Litten, Lawler, Storton.
Referee: Chris Kendall (RFL).