Wing Isa Nacewa scored the visitors' only try with Jonathan Sexton supplying 15 points with the boot.
The Scarlets, who came away with a losing bonus point, scored a try through Gareth Maule and two penalties and a conversion from Rhys Priestland.
It gave Leinster their 17th successive victory in the tournament and coach Joe Schmidt's 17th win from 19 Heineken Cup games.
Clermont Auvergne, last season's Heineken Cup semi-finalists, went back to the top of Pool Five thanks to a 13-minute burst at the start of the second half on their way to a 46-12 win at Exeter.
The visitors were quick off the mark at the restart, scoring 15 points to regain the lead - which they held on to and increased without reply.
Exeter will question the services of the TMO as their England flanker Tom Johnson appeared to have tackled Clermont Auvergne's centre Wesley Fofana - who went on to score a try in the corner early in the second half which changed the face of the game.
Saracens' dominant first half ensured their experiment of staging a home Heineken Cup match overseas was rewarded with a 30-13 victory over Racing Metro at King Baudouin Stadium.
The London club will be content to return to Brussels on the strength of a performance that puts them in control of Pool One, denying Racing a bonus point in the process.
Tries from Chris Wyles and Steve Borthwick put the 2011 Aviva Premiership champions in the driving seat, but their opponents were only fully subdued by Will Fraser's touchdown four minutes from time. A crowd of 18,202 saw the superb Charlie Hodgson kick 15 points, while Borthwick and centre Brad Barritt both enjoyed fine afternoons.
Racing touched down for the first time after Masi Matadigo and Juan Martin Hernandez combined to send winger Juan Imhoff scorching over and Hernandez converted, while former England back Olly Barkley and Gaetan Germain kicked over a penalty each.
Toulouse recorded their second win in Pool 2 with a 33-21 victory at Benetton Treviso.
Kristopher Burton kicked six first-half penalties for the hosts and added another after the break to give the Italians a 21-12 lead
But the Top 14 outfit scored a penalty try followed by touchdowns from Louis Picamoles and Vincent Clerc within the space of nine second-half minutes, all converted by Luke McAllister following his four earlier penalties, to avoid an upset.
Biarritz defeated Italian outfit Zebre 38-17 to move into second place and bounce back from a heavy defeat to Harlequins.
Fabien Barcella, Yann Lesgourges and Taku Ngwenya all picked up early tries as the French club started in impressive fashion and Pelu Taele's try after 45 minutes gave them a bonus point.
Two tries from Danny Care set Harlequins on their way to a deserved 30-22 Heineken Cup victory over Connacht at the Sportsground.
Eric Elwood's men ruined Quins' hopes of reaching the Heineken Cup knockout stages last January with a nail-biting 9-8 defeat at the Galway venue.
Nine months on, both sides threw off the shackles to share out 43 points in a free-flowing first half full of enterprising rugby.