Denmark's Asgreen, who won the Tour of California in May, edged out Stuyven after the pair had broken clear near the end of the 189km ride from Goettingen.
The Deceuninck Quick-Step man and Trek-Segafredo's Stuyven finished 17 seconds ahead of a group of 15 riders.
Sunday's final stage keeps the peloton in the Thuringian forest with an undulating course to Erfurt.