Ireland winger Jordan Larmour scored the game's only try for Leinster moments after both teams were reduced to 14 men as Jonathan Danty and Joe McCarthy were sin-binned following a 12th-minute tussle.
Harry Byrne nailed the conversion as Leinster replied to Antoine Hastoy's early penalty for the hosts in driving rain on the Atlantic coast.
Another Hastoy kick reduced the gap to a point, but Leinster took a 10-6 lead into half-time as Ciaran Frawley replaced Byrne and slotted over a penalty right after his introduction.
Hastoy again cut the deficit for La Rochelle but two more penalties from Frawley, the second a monster 60-metre effort with time expiring, secured victory for the Irish province.
Leinster are chasing a record-equalling fifth title after falling short against La Rochelle in successive finals. The French side won 27-26 last season to hoist the trophy in Dublin.
English Premiership leaders Sale produced a storming second-half display to beat a lacklustre Stade Francais in their opening Pool 2 fixture in Salford.
Leading 6-5 at half-time after Stade Francais captain Jeremy Ward had momentarily given his side the advantage, Sale stepped up a gear in the second half scoring 22 points unanswered with tries from Tom O'Flaherty, Jonny Hill and Sam Dugdale.
England fly-half George Ford opened the scoring with a penalty in the 13th minute before Ward found himself in space after a searing break from full-back Leo Barre to put Stade Francais, fifth in the Top 14, in front.
Ford, however, put Sale back in front just before halftime with his second penalty, this time from the 10-metre line.
Sale dominated the second period with Ford adding another penalty before left-wing O'Flaherty slipped through some flimsy tackling to score in the corner.
Ten minutes later, Sale found the same corner, this time with Raffi Quirke finding room for lock forward Hill to slide in.
Six minutes from time, Dugdale went on the charge from a tap penalty close to the French line and bulldozed his way through for the try.
Tom Curtis fired over the conversion to complete a fine afternoon for the English.
