Replacement prop Georges-Henri Colombe crossed in the 72nd minute as the French side triumphed in a rerun of last season's final.
The Irish province suffered a major blow with Michael Ala'alatoa's late red card in front of a sold-out Lansdowne Road.
Leo Cullen's Leinster eyed joining Toulouse on a record five titles but Ireland veteran Johnny Sexton watched on from the crowd due to an injury, denying him a final game for the province.
Ex-New Zealand scrum-half Tawera Kerr-Barlow started for La Rochelle after missing last year's win in Marseille with a hand injury
In front of a sea of home fans, Leinster made the best start possible as hooker Dan Sheehan opened the scoring from a smart lineout move after just 41 seconds.
Ross Byrne, standing in for 37-year-old Sexton, added the conversion to make it 7-0, with the Irish supporters in full voice even with the overcast conditions in front of 51,000 in Dublin.
Their dominance continued as they led 17-0, with winger Jimmy O'Brien scoring and Sheehan claiming his second by the quarter mark thanks to their clinical attack inside La Rochelle's 22m and almost perfect defence.
Thirty seconds before Sheehan's double, Kerr-Barlow was shown a yellow card.
La Rochelle's reaction came on 20 minutes as France centre Jonathan Danty crashed through three defenders to score from short range but the French joy was short-lived.
Revitalised La Rochelle
Byrne kicked two penalties to make it 23-7 after half an hour, either side of Kerr-Barlow's return from the sin-bin as Leinster captain James Ryan left the field with a head injury.
With two minutes left of the first half, Ronan O'Gara's French side cut the deficit to 23-14 as Samoa centre UJ Seuteni sliced through Leinster's defence after some trademark powerful carries from lock Will Skelton and prop Uini Atonio.
After the break, Antoine Hastoy kicked two penalties either side of a Byrne effort to make it 26-20 with half an hour to play as French fans around the ground found their voice.
Going into the closing quarter of an hour the tension mounted and Hastoy found touch with a penalty five metres from the Irish line.
With eight minutes remaining, and after countless pick and goes, Colombe bundled over for the French side.
Hastoy's conversion made it 27-26 and La Rochelle led for the first time of the enthralling encounter.
After Danty was sin-binned for a high tackle, Byrne kicked the ball within 20 metres of La Rochelle's whitewash.
Inches from the French line and with Leinster on top, Ala'alatoa was sent off with less than two minutes remaining for a dangerous clear-out on Colombe.
With 15 seconds over the 80 minutes Hastoy kicked the ball dead to end the final and give La Rochelle back-to-back title triumphs.
