Nice scored first through a fifth minute penalty but Leinster soon gained an advantage through winger Simon Keogh who scored a try, seven minutes later, after good work from centre Isa Nacewa.
Leinster piled on the pressure with Malcolm O'Kelly putting in an excellent shift in a dominant pack and on 24 minutes Kevin McLaughlin displayed good strength to score his side's second try, which Nacewa converted, to push Leinster into a 12-3 lead.
Debutant Berne then scored a deserved try, four minutes later, to give the Irish side a 17-3 half-time lead.
Leinster continued their try-scoring ways in the second half and replacement scrum half Chris Keane touched down in the 45th minute. Nacewa again converted to push the lead to 21 points.
Replacements used: Chris Keane for O'Donohoe (32 mins), Paul Ryan for Jennings, Leo Cullen for O'Kelly, Ronan McCormack for Ross, Shane Horgan for Monahan, Billy Ngawini for Simon Keogh (all half-time), Jason Harris-Wright for Fogarty (56), David Moore for Keane, Simon Keogh for Macken, Shane Monahan for Morris (all 61), Eoin Sheriff for McLaughlin (66), Shane Jennings for Hogan (68), John Fogarty for Harris-Wright (72).