Jonathan Sexton, the hero against Benetton Treviso, slipped through for an eighth minute try to get them off the mark against Michael Bradley's men.
But Edinburgh, winless in Dublin for seven years, came to the fore in the second quarter with Greig Laidlaw rewarding them with a brace of penalties.
That left Leinster hanging on to a 10-6 lead at the break and although Macken's tries extended the advantage, Edinburgh showed great resolve to take the game right down to the wire.
The Scots bounced back from two sin-binnings to grab a late try from South African prop Willem Nel, ensuring a nervy finish for the home side.
Proceedings began on a sombre note as a minute's silence was impeccably observed in honour of Ulster's Nevin Spence, who died tragically last weekend.
Jamie Roberts scored his first try for Cardiff Blues since May 2010 as they consolidated their place in the top half of the RaboDirect Pro12 table with a 34-18 win over Benetton Treviso at the Arms Park.
The Wales centre's last score for his region came against Toulon in the final of the Amlin Challenge Cup.
And he was delighted to touch down as they saw off a gutsy Treviso, who made them fight every inch of the way.
The Italians plugged away but the Blues got a fourth try, replacement prop Campese Ma'afu the scorer, in the final minute to also pick up a precious bonus point in front of a crowd of 8,133.
It was Treviso's third defeat of the league campaign, their sole victory coming over champions Ospreys, while it was the Blues' third success in four attempts.
Munster got back on the winning trail in the RaboDirect PRO12 by running five tries past the Newport Gwent Dragons in a 33-13 victory at Thomond Park.
Rob Penney's men started like a train, working Ian Keatley and Niall Ronan over for converted tries inside 13 minutes.
Tom Prydie and Lewis Robling kicked a penalty apiece for the visitors to cut the gap to 14-6 by half-time, but tries from Conor Murray and Simon Zebo - while Dragons prop Dan Way was in the sin-bin - strengthened Munster's hand, although Dan Evans grabbed one back for the visitors.
But with the bonus point in the bag, Munster signed off in style with a swashbuckling score for Tommy O'Donnell with eight minutes left.
- Cardiff Blues