The Rhinos went into the game with nine players missing through injury, including reigning Man of Steel Jake Connor, but edged ahead early on as Chris Hankinson's penalty was their reward for sustained pressure as Leigh struggled with the new, stricter interpretation of the ruck rules.
After that ragged start, the Leopards burst into life as Ipape broke, Bailey Hodgson injected pace and Lam had the presence of mind to hurl a pass to Senior for a good finish on his Super League debut for the hosts.
Ipape was causing havoc and when he led another attack and fed Joe Ofahengaue, the Papua New Guinea international was on hand to grab the offload and force his way over.
Any words of hope from Leeds coach Brad Arthur at half-time quickly dissipated as, from the restart, Riley Lumb dropped the ball and Hughes kicked ahead to score, with Davis adding another as the Rhinos defence again wobbled.
Jenkins burst through two tackles to expose the Leigh defence for the first time and score, and with a glimmer of hope Leeds went forward.
Newman furiously claimed his eye had been gouged following a tackle and with tempers fraying he was sin-binned shortly afterwards following a clash, with Davis following him for his part in the melee.
Another Lumb error handed Leigh territory and Ipape dummied to go right, switched left, and Lam gathered his pass and swivelled out of Tom Holroyd's attempted tackle to seal the win, although Croft gave Leeds' travelling support something to cheer late in the game.