New Zealand's double Rugby World Cup winner Jerome Kaino said it was "awesome" to reach his first European Champions Cup final after joint-record four-time winners Toulouse's 21-9 home win over Bordeaux-Begles on Saturday.
France scrum-half Dupont crossed late against an away side playing their first game since an April 11 quarter-final victory over Racing 92 because of eight cases of coronavirus in their squad.
The hosts, who last won the competition in 2010, will face either La Rochelle or fellow four-time champions Leinster, who play on Sunday, in the final at Twickenham on May 22. Toulouse lost in the last four the past two seasons.
"We've been building these last few years and have tripped up in the semi-final stages so I'm very proud. It's an awesome feeling to be able to step into the door and make the final," back-rower Kaino, who will retire at the end of season, told broadcasters Channel 4.
"We were under no illusions it was going to be easy. We knew we were up for it and they weren't going to just lie down," he added.
Toulouse coach Ugo Mola recalled 38-year-old loose forward Kaino who had been rested since the last-eight win over Clermont three weeks ago.
Visiting coach Christophe Urios made six changes from the win against Racing last month, with former France captain Jefferson Poirot, who was among those to catch the virus, starting on the bench.
At a rain-sodden Stade Ernest-Wallon, Urios' men, making their first European semi-final appearance, led 3-0 within three minutes after Matthieu Jalibert's penalty goal.
Toulouse responded, defying difficult conditions as the Top 14's leading try scorer Matthis Lebel crossed in the corner.
Lebel, 22, claimed his 15th try of the season after ambitious passes from Romain Ntamack, celebrating his 22nd birthday, and Maxime Medard, making his 350th club appearance.
Ntamack, who reclaimed the France No. 10 jersey for the final game of this year's Six Nations from Jalibert, missed the conversion.
The two stand-offs traded shots at goal and Toulouse led 8-6 at the break despite Bordeaux-Begles' control.
The downpour stopped and the sun broke through as Ntamack kicked another penalty to make it 11-6 after 45 minutes.
Mola's men took a patient stranglehold on the tie before Ntamack and Jalibert were both succesful with shots at goal as the hosts led 14-9 with 10 minutes to go.
With a place in the final on the line, the game opened up as the home side began to impose their open style of play.
Their possession was rewarded with seven minutes remaining as Medard freed his arms in a tackle and off-loaded to Zack Holmes, who found Dupont for his 16th try, for club and country, of the season.
Ntamack slotted the extras. As the clock moved into the red, the fly-half kicked to touch with to end the game and send Toulouse to their first final in more than a decade.