La Rochelle won the Champions Cup for the first time in hugely dramatic fashion as Arthur Retiere's 79th-minute try saw them edge Leinster 24-21.
Leinster had to defend heroically in the latter stages in Marseille but their defence was eventually breached as Retiere stretched to touch down.
They had led for much of the game thanks to six Johnny Sexton penalties and one from Ross Byrne.
Raymond Rhule and Pierre Bourgarit had crossed for La Rochelle's other tries.
The triumph delivers a first major trophy for La Rochelle, who became the 13th side to win the Champions Cup and the fourth from France.
The French side had beaten Leinster at the semi-final stage last season, but lost to Toulouse in the showpiece, so this will go some way to make up for that disappointment.
Their coach Ronan O'Gara, the tournament's record points scorer, joins his Leinster counterpart Leo Cullen and Toulouse's Ugo Mola as the only men to win the championship as a player and a coach.
The Irish province were frustrated, however, in their bid to equal Toulouse's record of five wins in Europe's premier club competition.
Leinster enjoyed the better of the early stages and were rewarded with two Sexton penalties in the opening nine minutes, the French side being punished for their indiscipline, firstly for hands in the ruck and then offside.
O'Gara's team responded a minute later when wing Rhule powered over the line, with Ihaia West converting.
Robbie Henshaw had been too slow to roll away from a tackle but advantage was played and La Rochelle passed the ball quickly through the hands. Dillyn Leyds' offload set Rhule on his way to weave past Hugo Keenan and other defenders before diving over.
Sexton restored his side's lead with his third penalty in the 22nd minute after their opponents were punished for crossing in midfield, but the Irish side had to endure a period of pressure in the run-up to the interval.
La Rochelle stretched their opponents, attacking from side to side but suffered from a lack of composure at vital stages as they advanced on the line.
Two vital scrums before half-time, one at either end of the pitch, both went in Leinster's favour, and Sexton knocked over a fourth penalty in added time.
La Rochelle reduced their deficit two minutes into the second half as West landed three points after Caelan Doris failed to release, but two further penalties from Sexton made the Top 14 side pay for a lack of discipline.
Feeding off the energy of the partisan crowd at Stade Orange Velodrome, La Rochelle drew themselves to within a point when they won their own line-out, put together an attacking maul and Bourgarit rumbled over to touch down, West adding the extras.
Five minutes later French second row Thomas Lavault was shown a yellow card by referee Wayne Barnes for a blatant off-the-ball trip on Jamison Gibson-Park and replacement Ross Byrne, who had just come on in place of a hobbling Sexton, kicked over a penalty.
Despite their numerical disadvantage, La Rochelle proved dominant up front and enjoyed a sustained period of territorial possession, earning a series of penalties, but were repeatedly frustrated in their efforts to score as they kicked for the corner and then took a scrum.
Their patience was eventually rewarded when replacement scrum-half Retiere stretched and dotted the ball down on the line for the crucial score. West contributed the additional two points to secure an unforgettable success after a thrilling game.
Leinster: Keenan; J O'Brien, Ringrose, Henshaw, Lowe; Sexton (capt), Gibson-Park; Porter, Kelleher, Furlong, Molony, Ryan; Doris, Van der Flier, Conan.
Replacements: Sheehan, Healy, Ala'alatoa, McCarthy, Ruddock, McGrath, R Byrne, Frawley.
La Rochelle: Dulin; Leyds, Sinzelle, Danty, Rhule; West, Berjon; Priso, Bourgarit, Atonio, Lavault, Skelton; Liebenberg, Haddad, Alldritt (capt).
Replacements: Bosch, Wardi, Sclavi, Sazy, Bourdeau, Retiere, Botia, Favre.