The defending champions struggled to cope with the pace of the hosts’ attack, with James Lowe, the tournament’s top-scorer this season, claiming two of their four tries.
The unrelenting speed of Leinster’s play left Toulouse, a week on from their penalty shootout heroics here in Dublin, scrambling to plug leaks and they also lost lock Emmanuel Meafou to the sin bin.
Nonetheless, Tadhg Furlong’s 16th-minute injury-enforced departure was a big blow for the Irish province, with their scrum targeted by Cyril Baille and company.
Lowe’s 49th-minute effort – his 10th of the European campaign – was cancelled out by Toulouse replacement Selevasio Tolofua with 15 minutes remaining.
Ugo Mola’s men kept plugging away, but a closing try from Hugo Keenan, on the back of a Ross Byrne penalty, sealed Leinster’s place in the May 28 decider against either Racing 92 or La Rochelle.
An early Leinster barrage had Toulouse backpedalling, Matthis Lebel doing well to deny Jimmy O’Brien a try before Sexton fired over a penalty.
However, just as the hosts threatened again through Keenan, Dupont blocked Jamison Gibson-Park’s kick and broke free from the Toulouse 22 for a sucker punch score, converted by Thomas Ramos.
Sexton narrowed the gap to 7-6 and, while a break from Caelan Doris had promised more, Leinster were ruthless on the quarter-hour mark.
A lineout maul gave them momentum, Robbie Henshaw carried strongly and Sexton’s inside pass saw Lowe score a seven-pointer on the short side.
Ross Molony sent Sexton through the Toulouse defence just three minutes later, with the fly-half finding Van der Flier, who rolled over the line despite Juan Cruz Mallia’s tackle.
Despite Sexton stretching the lead to 20-7, Toulouse stormed back with a big scrum and Ramos duly cut the deficit.
Sexton punished Francois Cros for going off his feet and, although a cynical Meafou saw yellow following a Garry Ringrose surge, Toulouse survived thanks to an offside call against Henshaw.
The French giants stood firm while down to 14 men, but Leinster stunned them with a try off a Molony lineout steal.
Gibson-Park followed up to charge down Mallia and the attacking waves ended with Sexton’s long pass putting Lowe over on the left.
The gap was out to 20 points after Sexton’s well-struck conversion and Toulouse’s initial attempts off a maul were repelled.
Pita Ahki lifted the Top 14 title holders with a man-and-ball tackle on Sexton and the visitors’ forward power allowed Tolofua to tiptoe over from a lineout drive, with Ramos converting.
Leinster replacement Byrne knocked over the insurance score, though, and Keenan slipped past both Peato Mauvaka and Baille with two minutes left, ensuring Leinster will have a shot at a fifth European star in Marseille.