Tinning, who is heading to the US to play for defending champion Europe in next weekend's Solheim Cup, finished with a 72-hole total of 273, 15 under par on the Kokkedal course near Copenhagen.
England's Laura Fairclough closed with a 66 to finish second. Cecilia Ekelundh of Sweden, who led overnight, slipped to a 70 and took third a further shot back.
It was Tinning's third Ladies European Tour win of the season.
"Obviously winning in your own country is an amazing feeling and the crowd was fantastic," said Tinning, who leaves Monday for Crooked Stick at Carmel, Indiana, site of the Solheim Cup.
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