Scrum-half Dupont, 27, made his contributions early in the second half as the holders claimed both trophies in one season for a third time with a record score.
Bordeaux-Begles had just one Maxime Lucu penalty on the scoreboard as they conceded nine tries in their first appearance in a final in either competition.
"I'm very happy, it's incredible for the history of the club and these guys," Dupont told Canal+.
"I think I've achieved much more than I could have dreamt of as a child.
"I have to realise that but not too much as to keep dreaming," the 2021 World Rugby player of the year added.
Humid and warm conditions in front of a sold-out 67,000-capacity Stade Velodrome welcomed both sides, with Paris’ Stade de France out of use due to the upcoming Olympic Games.
Bordeaux-Begles were handed a big boost as France fly-half Matthieu Jalibert and Tonga loose-head prop Ben Tameifuna were passed fit after they had missed last Saturday’s semi-final win over Stade Francais.
Toulouse started without first-choice loose-head Cyril Baille, who suffered a serious ankle injury in the last four victory over La Rochelle.
Giant front-rower Tameifuna wore a Tongan flag as the French national anthem rang around the Velodrome with French president Emmanuel Macron absent.
Toulouse were quick out of the blocks as Dupont crossed after just six minutes in his final game before France's Olympic sevens squad is named on July 8.
In the build-up to the try, the video referee adjudged Bordeaux-Begles' No 8 Tevita Tatafu had made a high tackle and referee Ludovic Cayre showed the Japan back-rower a yellow card.
By the time Tatafu had returned to the field Toulouse led 10-3 after 16 minutes as full-back Thomas Ramos added to his conversion of Dupont’s first touchdown with a penalty in response to Maxime Lucu’s three-pointer for Bordeaux-Begles.
Total control
By the 25-minute mark Toulouse and a majestic Dupont were in total control.
Dupont set-up hooker Peato Mauvaka with a flat pass before scoring a second with a delightful chip kick and Ramos' conversion made it 22-3.
Bordeaux-Begles in their maiden Top 14 final, coached by former Toulouse hooker Yannick Bru, were struggling with flankers Jack Willis and Francois Cros in superb form in defence for the champions.
Ramos extended the lead to 25-3 four minutes after the interval with a second penalty as Toulouse played up to their pre-match favourites tag.
With 25 minutes to go a tired-looking pair of Jalibert and Tameifuna had been replaced with Toulouse's red and black clad fans sensing another Bouclier de Brennus title, first awarded in 1892.
Victory was confirmed with a quarter of an hour left as Ramos dived over, his try coming from a Dupont break.
A cruising Toulouse added a fifth and sixth try as hooker Julien Marchand and winger Blair Kinghorn crossed with ease before the loudest cheer of the game came as Dupont was replaced with 10 minutes to play.
Kinghorn's try took Toulouse to 40 points and the record score in a Top 14 final.
Toulouse rubbed salt into Bordeaux-Begles wounds in the closing five minutes as Ramos added a second try, prop David Ainu’u and full-back Ange Capuozzo crashed over to cross the half century.
