Cort, 30, completed the 203.1 kilometres between Faro and Tavira in 05:05.14 hours, beating Italian Filippo Ganna (INEOS) in second, and Belgian Jordi Meeus (BORA-hansgrohe) third, with Rui Oliveira (UAE Emirates) sixth and Rui Costa (Intermarché-Wanty-Circus) in seventh.
Overall, the Dane now has an 18-second lead over Rui Costa, who is second, and 20 seconds behind Belgian Ilan Van Wilder (Soudal-QuickStep), third.
On Saturday, the fourth and penultimate stage of the 49th edition connects Albufeira to the top of Malhão in 177.9 kilometers, before Sunday's decisive time trial in Lagoa.