Isa Nacewa landed the match-winning penalty in the 78th minute, but Leo Cullen’s men had to survive a frantic finish, at the end of which Racing replacement fly-half Remi Tales pushed a drop-goal effort wide.
Racing shrugged off injuries to fly-halves Dan Carter and Pat Lambie to lead twice during a cagey first half, Teddy Iribaren’s two penalties being cancelled out by a Jonathan Sexton brace. The 6-6 scoreline became 9-9 and then 12-12 as Iribaren landed four of his five penalty attempts and Sexton finished with three.
It was left to the retiring captain Nacewa to bring Leinster level, before an offside decision against Tales allowed the 35-year-old winger to boot the Blues to their first European title since 2012.
The Irish province now jointly hold the record for most European Cups won along with Toulouse, while Cullen is the first man to win the tournament as both a player and a coach.
Nacewa, Cian Healy, Sexton and Devin Toner all collected a record-equalling fourth title.
A pre-match hamstring injury spoiled Carter’s European swansong, with Racing’s injury list already including talismanic skipper Maxime Machenaud (knee) and Dimitri Szarzewski (bicep).
Lambie’s final lasted just under three minutes, the South African stand-off damaging his knee on an early break which led to Iribaren’s opening penalty from 45 metres out.
Sexton levelled in the 16th minute following his own loop with Scott Fardy and a penetrating run from Nacewa, but Iribaren, who impressed along with Camille Chat in a composed first quarter from Racing, punished a maul infringement for 6-3.
Although struggling to produce quick ruck ball on the greasy surface, Leinster had the edge under the high ball through Rob Kearney.
James Ryan’s high work-rate launched Leinster forward to win a kickable penalty, only for Sexton’s tap-and-go to end in a relieving breakdown penalty poached by hooker Chat.
Sexton made no mistake with a 38th-minute effort from the tee, following a deliberate knock-on by Leone Nakarawa.
Iribaren’s right boot restored Racing’s lead five minutes after the restart, rewarding a bruising set of carries from his pack. Sexton slipped in his attempts to respond with a difficult 48-metre penalty.
The Ireland fly-half nailed his next effort to square things up again in the 53rd minute. Sexton suffered his second miss from long range, following a James Ryan lineout steal, and as the contest became increasingly scrappy, Iribaren’s only penalty miss let Dan Leavy off the hook for a high tackle.
Referee Wayne Barnes’ whistle was far too influential for both sides’ liking, the stop-start fare leading to successful place-kicks from Iribaren and Nacewa late on. Crucially, it was Racing who blundered when Teddy Thomas was tackled into touch, and Nacewa took full advantage of Tales’ subsequent offside to claim a very hard-earned victory.