It marked a first World Tour stage race victory for the 23-year-old Spaniard who finished seven seconds ahead of Alexandre Vlasov in the general classification.
The Russian was a further two seconds clear of German rookie Florian Lipowitz, his Bora teammate.
Rodriguez took the overall lead when he finished third in Saturday's mountainous 'queen' stage and had little difficulty in maintaining it in the straightforward 150.8km final stage.
He was content to stay in the peloton, surrounded by his Ineos team-mates, including Colombian Egan Bernal.
Rodriguez showed his potential last year by winning a mountain stage of the Tour de France in Morzine and then finishing fifth overall in Paris on his first appearance.
In early form this season, he won the final stage of the Tour of the Basque Country three weeks ago and took second place overall.
Sunday provided a second stage win of the race for French rider Godon (Decathlon-AG2R La Mondiale), who had already won the opener on Wednesday.
"Cycling is all about spirals and confidence," the 27-year-old told L'Equipe. "My team-mates did a great job for me."
