Rhinos were on top throughout, scoring five tries to two - and they would have won by a wider margin but for some superb last-ditch defence by the home team.
Rhinos had a player held up over the line four times and survived 10 minutes with only 12 men after Ryan Hall was sin-binned for the first time in his career, early on.
Joel Moon scored the opening try before Hall made amends by crossing for a touchdown which was improved by Liam Sutcliffe.
Cas struck back when Michael Shenton touched down from Liam Finn’s kick, but Stevie Ward scored in similar fashion from a grubber by Sutcliffe, whose goal made it 16-6 at the break.
Hall’s second try, with 18 minutes left, edged Rhinos further in front and Adam Cuthbertson stretched over to cap a fine game with a try which was improved by Sutcliffe.
Shenton scored a second try after a one-two with Justin Carney, Luke Gale landing his second goal, but it was too little, too late.