Leinster (18) 28
Jamie Heaslip (left) scored one of Leinster's tries at the RDS
Tries: Heaslip, Gleeson, Contepomi
Cons: Contepomi 2
Pens: Contepomi 3
Edinburgh (3) 14
Pens: Godman 2, Blair
Leinster claimed their expected Heineken Cup win over Edinburgh but the Irish province could rue their failure to secure a bonus point.
Tries from Jamie Heaslip and Keith Gleeson helped the home side into a 18-3 lead by half-time.
John Houston's try gave Edinburgh hope and the visitors were still within a score of Leinster as Contepomi and Phil Godman swapped penalties.
Contepomi's try extended Leinster's lead but the fourth try proved elusive.
The Magners League leaders had an early effort from full-back Rob Kearney ruled out by television match official Daniel Gillet and Edinburgh held firm at 3-3 after penalties from Contepomi and Godman.
Leinster regained the lead in the 16th minute when Edinburgh's defence was ruthlessly exposed and Heaslip powered over the line from close range.
After Contepomi's conversion, scrum-half and captain Mike Blair tried to inspire an Edinburgh revival but they made no headway on the scoreboard.
Another Contepomi penalty extended Leinster's lead to 10 on the half-hour and it then got even better for the home side with Brian O'Driscoll's initial break setting up Gleeson's try.
Trailing 18-3 at the interval, Edinburgh battled gamely after half-time.
After a Godman penalty miss, winger Houston charged over for an Edinburgh try after good work by Ross Rennie and the lively Nick De Luca.
As Leinster lost their way, they were unable to even exploit Calum MacRae's sin-binning as the Scots answered Contepomi's third penalty with two successes from Godman and a David Blair kick.
However, a Gordon D'Arcy burst paved the way for Contepomi to score Leinster's third try and the Argentine star added the extras.
Nonetheless, the hosts' push for a bonus point never really came and it was Edinburgh who got closest to the whitewash late on when replacement Ben Meyer almost sniped over.
Leinster: Kearney; Horgan, O'Driscoll (cpt), D'Arcy, Fitzgerald; Contepomi, Willis; le Roux, Jackman, Wright, Cullen, O'Kelly, Keogh, Gleeson, Heaslip.
Replacements: Jennings for Keogh 48.
Not used: Blaney, Knoop, Jowitt, Keane, Sexton, Brown.
Edinburgh: Cairns; Turnbull, De Luca, Dey, Houston; Godman, M Blair (cpt); Jacobsen, Ford, Kerr, Mustchin, Gissing, Reid, Rennie, Callam.
Replacements: MacRae for Dey (49), D Blair for Godman (60), Meyer for M. Blair (76), Allori for Kerr (38), S Cross for Reid (53).
Not Used: Kelly, Hamilton.
Referee: Romain Poite (France).