Leigh duo Peter Mata'utia and Matty Dawson were sent off as Leeds rammed home their Super League quality to win 52-22 and march into the Ladbrokes Challenge Cup semi-finals.
Centurions full-back Mata'utia made a dangerous lift on Rhinos hooker Matt Parcell in the 10th minute and was given his marching orders by referee Chris Kendall before winger Dawson followed suit for dissent in the closing stages.
Leigh had struck first through prop Nathan Mason's close-range score but Brian McDermott's side took control after Mata'utia's sending off and led 40-12 at the break.
They ran in a total of seven first-half tries to seal their place at the Macron Stadium in Bolton for the Challenge Cup semi-finals on August 5 as part of a historic double-header.
Leeds had beaten Leigh at this stage of the competition in 2012 and 2014 and this latest meeting was switched to the home of Featherstone Rovers because of the Test match cricket taking place at Headingley.