The victory in Riyadh gives Inter a chance to win the trophy for the fourth successive time.
The first half ended scoreless, mostly thanks to the heroics of Atalanta keeper Marco Carnesecchi, but Inter found the breakthrough four minutes after the break through Dumfries.
Dumfries scored first with an acrobatic overhead kick from close range then finished off a counterattack with a long-range strike.
Inter then survived some late pressure from current league leaders Atalanta to see out the win.
Atalanta surprisingly kept Ademola Lookman, Charles De Ketelaere and Ederson on the bench at the start.
The three players came on near the hour mark and Ederson had a potential goal waved off for offside after a VAR check.
Inter beat Atalanta 4-0 twice in Serie A last year, in February and August.
This season, Atalanta and Napoli currently hold a one-point lead over Inter, who have a game in hand.
The only negative note for Inter was that Marcus Thuram exited with an apparent left thigh issue at halftime.
Juventus and AC Milan play in the second semi-final on Friday with the final scheduled for Monday.
with AP
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