Isa Nacewa had the Irish province ahead but Tobie Botes threaded two penalties and Chris Burton landed a pair of drop-goals to put the Italians 12-10 up at the break.
New Zealander Nacewa continued to outshine the returning stars and had Leinster back in front only for Botes to sink another penalty and Luke McLean to race home for a try and extend the lead.
And any hopes Leinster had of halting a shocking start to the season were ended when Brendan Williams charged clear at the death to seal a 29-13.
Wales wing Leigh Halfpenny was one of three tryscorers for Cardiff as they picked up a bonus point 43-21 victory against Newport-Gwent Dragons.
Halfpenny opened the scoring for the Blues while Rhys Thomas' double ensured the hosts lead 20-6 at half time.
The Dragons hit back after the break with Will Harries and Adam Hughes crossing the whitewash and the trusty boot of fly-half Matthew Jones keeping the scoreboard ticking over.
But Cardiff sealed the win - and a bonus point for the fourth try - when Xavier Rush scored form a quickly-taken penalty.