Leinster, chasing a record-equalling fifth title, ultimately paid for their failure to score a try – not that it appeared to matter as Sexton converted two straightforward penalties to edge them ahead.
Rhule then bundled over in the left corner after Dillyn Leyds' offload, before another Sexton penalty put Leinster back on top, and he profited again before the break when La Rochelle were punished for more sloppiness.
West reduced the arrears with three points after the interval, but Sexton responded with a further two penalties to take Leinster out of reach of a converted La Rochelle try.
That lead was cut after 61 minutes, however, as Bourgarit crossed following a maul and West's conversion made it a one-point game.
Sexton limped off in the aftermath of that try, but La Rochelle's momentum appeared to be halted when Lavault was yellow-carded for tripping Jamison Gibson-Park, allowing replacement Byrne to dispatch the subsequent kick.
And yet there was still time, with a prolonged period of La Rochelle pressure ending in Retiere breaking through to claim Champions Cup glory for his side at the second time of asking.
