Costa headed Toulouse in front inside four minutes, adding a second in similar fashion before Dallinga bagged a brace with barely half an hour played at the Stade de France.
Zakaria Aboukhlal rounded off a memorable triumph for Toulouse late in the second half after Ludovic Blas struck a consolation from the spot for Nantes.
However, Toulouse risk being unable to play in Europe next season if AC Milan qualify for the Champions League or Europa League as both clubs are owned by US investment firm RedBird Capital Partners.
President Emmanuel Macron shook hands with players in the tunnel before the game, sidestepping fears of a hostile reception following his hugely unpopular pension reform, which has sparked three months of protests and strikes.
Toulouse are enjoying a fine season on their return to Ligue 1, sitting comfortably mid-table while reaching the final for the first time in 66 years.
Their 6-3 win over Angers in 1957 remains the competition’s highest scoring final, but the club disappeared a decade later in a merger and a new version was founded in 1970.
Facing a Nantes side locked in a battle for their top-flight survival, Toulouse immediately seized control through an unlikely hero as Costa scored his first two goals of the season inside 10 minutes.
The Cape Verde centre-back, who has featured almost exclusively in the cup this season, outmuscled Andrei Girotto to power in the opening goal from Branco van den Boomen’s corner.
Van den Boomen was again at the origin of Toulouse’s second, the Dutch midfielder’s free-kick hooked back across goal by Stijn Spierings for Costa to nod emphatically past Alban Lafont.
Nantes striker Mostafa Mohamed had an effort hacked off the line by Gabriel Suazo after Toulouse goalkeeper Kjetil Haug flapped at a corner.
Toulouse soon increased their advantage as Suazo curled a superb ball through for Dallinga to lift over the advancing Lafont.
Dallinga then pounced on a rebound after Fares Chaibi’s shot was parried tamely towards the Dutch striker by Lafont, all but killing off any suspense with just 31 minutes gone.
Nantes pulled one back in the second half after Rasmus Nicolaisen fouled Fabien Centonze in the area.
Blas, who smashed home the winner from the spot in last year’s final against Nice, did so again, but this time it was scant consolation for the Canaries.
Aboukhlal capped off a glorious night for Toulouse by drilling home a fifth from the edge of the box, sparking wild celebrations from their purple-clad fans while leaving a demoralised Nantes needing to quickly lift themselves to avoid the double misery of relegation.
AFP
