Leigh gave a good account of themselves and gave the Rhinos a game for twenty five minutes. Skipper Kevin Sinfield was the man-of-the-match as he kicked 10 from 10 and scored a brace to help himself to 28 points.
Rob Burrow, Ben Jones-Bishop, Shaun Lunt, Ryan Hall 2, Brent Webb, Danny McGuire and Lee Smith all crossed for Leeds.
The Championship side managed a try in each half through Gregg McNally and Tommy Goulden, with Martyn Ridyard adding the extras.
On Saturday afternoon holders Wigan Warriors booked their place in the last four with an 18-4 hard-fought win over local rivals St Helens at the DW Stadium.
It was a scrappy affair and Saints made the better start with Paul Wellens scoring inside the first ten minutes.