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The win saw Michael Cheika’s side erase some memories of their Heineken Cup collapse to Edinburgh.
Ulster were under the cosh from the start and only some aggressive defending, typified by livewire lock Ryan Caldwell and Ireland flanker Neil Best, kept their try-line intact.
Leinster adopted a direct style, establishing early dominance at the scrum and foraging around the fringes, with young fly-half Sexton also peppering the touchlines with some fine kicks.
Leinster went ahead in the ninth-minute when Contepomi knocked over a close range penalty and while he was kept quiet in open play, the Ulster defence was almost unlocked on the half-hour when the Argentinian combined superbly with Sexton and Keith Gleeson.
Winless in Dublin since 1999, Ulster kept themselves in touch with some teak-tough tackling and centre Andrew Trimble began to find space midway through the half.
A better-placed pass would have put the Ireland international away in the 24th-minute and it took a brilliant tackle from Gleeson to fell Trimble when he threatened again just moments later.
A subsequent ruck infringement allowed Contepomi to double Leinster’s lead and the Pumas star kept up his 100% record in the 29th-minute, after Ulster scrum half Isaac Boss had been sin-binned.
Paddy Wallace had a chance to cut the gap for Ulster at the start of the second but his wind-backed effort fell short of the uprights.
Ulster were back to 14 men soon after when flanker Neil Best was yellow carded for a blatant foot trip on Sexton. Worse followed for the visitors as they lost their captain Rory Best to a leg injury.
Leinster began to motor clear on the scoreboard with Contepomi’s fourth penalty being followed by Healy’s 57th-minute try.
The young prop, part of the successful Ireland Under-20 Grand Slam team from last season, fooled Wallace with a lovely step and he straightened to make the line from 10 metres out.
Contepomi converted and knocked over another penalty before the seal was put on Leinster’s fourth successive league win when Sexton’s snappy pass sent number 8 Heaslip charging through a gap and in behind the posts.