Leeds trailed 6-0 when Championship side Leigh Centurions had full-back Peter Mata’utia sent off for a dangerous tackle on Matt Parcell.
Rhinos exploited their extra man to run in seven first-half tries as they took a 40-12 interval lead en route to a comprehensive success.
In the opening exchanges it looked like the Super League side might have their hands full, but the red card changed the game.
Playing up the slope at Featherstone Rovers’ Post Office Road, Nathan Mason crashed over from close range after just four minutes and Ben Reynolds converted to five Leigh a 6-0 lead.
But referee Chris Kendall had no choice but to dismiss Mata’utia just four minutes later and from then on Rhinos were always in command.
A kick from Jordan Lilley bounced away from Mata’utia and straight to Parcell.
He collected, but was grabbed by the Leigh man, up-ended and dropped on his head and neck.
Rhinos scored in the set from the penalty, then ran in five successive tries without Leigh having possession of the ball to make it 34-6 after 27 minutes.
The sides swapped tries before the break, but the game petered out after Leeds scored first in the second half.
Leeds coach Brian McDermott described it as a “pretty good” win and performance.
He reflected: “They are a good team, they had some form coming into this game and they’ve got a lot of players with Super League experience.
“I think the gap between the top Championship teams and the Super League teams is as close as it’s ever going to get for a while.
“The form we are in at the moment and some of the injuries we’ve got and some of the injuries we’ve incurred (last night), it was a pretty solid performance.
“It was a tough performance. We showed some toughness, which we probably haven’t been showing in recent weeks.”
McDermott, whose side are on a three-game losing run in Super League, felt Mata’utia’s red card was a major factor in the game, but was justified. “You can argue he’s been one of their best performers so far this year,” he said.
“The fact he left the field made it an easier day for us, I’ve no drama admitting that. I don’t think the player meant to do it, but it was a sending-off.”
Tom Briscoe crossed for Leeds’s opening two tries and Jack Walker, Ash Handley, Jimmy Keinhorst, Ashton Golding and Richie Myler also touched down before half-time.
Drew Hutchison pulled a try back, but when Cameron Smith crossed for his first Leeds try soon after the interval there was no way back.
Ben Crooks and Liam Hood scored consolation tries and Reynolds finished with three goals, but Adam Cuthbertson’s touchdown on the final play completed the scoring.
Jordan Lilley booted seven conversions and a penalty.
The game ended 12 versus 10 with Leeds’s Brett Ferres sin-binned alongside opponent Jamie Acton and Leigh’s Matty Dawson-Jones sent off for dissent in the final seconds.
Injuries took the gloss off Rhinos’ win with Parcell (head), Carl Ablett (calf) and Keinhorst (hamstring) all going off inside the opening 30 minutes, leaving Leeds with just one available substitute.
The tie was staged at Featherstone due to Test cricket making Headingley unavailable.
Leeds Rhinos: Walker, Briscoe, Keinhorst, Handley, Hall, Lilley, Myler, Cuthbertson, Parcell, Oledzki, Ferres, Ward, Ablett. Substitutes: Mullally, Smith, Walters, Golding.
Leigh Centurions: Mata’utia, Dawson, Crooks, Hall, Evans, Reynolds, Hutchison, Acton, Hood, Mason, B Thompson, Hansen, J Thompson. Substitutes: Richards, Higham, Baldwinson, Larroyer.
Referee: Chris Kendall (RFL).