The first race in the final face-off between the pair was abandoned after Morton appeared to have a problem with her bike but the German was unperturbed, winning the next two races against her rival to sweep the gold.
Probably the most popular medal winner was Hong Kong's Wai Sze Lee, who won the bronze in front of a jubilant home crowd.
On a good night for Australian cycling, Queenslander Jordan Kerby held off a strong challenge from Italy's Filippo Ganna to take gold in the men's 4km individual pursuit, with his 18-year-old countryman Kell O'Brien picking up the bronze.
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Another Australian, Cameron Meyer, dominated the men's points race, leaving the field in his wake to win by 36 points from Belgian Kenny De Ketele, who won silver with a last-ditch sprint to beat Wojciech Pszczolarski of Poland into third place.
Britain's Katie Archibald dug deep after a poor start to secure a stunning victory in the women's omnium, adding a world title to the gold medal she won in the team pursuit event at the Rio Olympics last year.
Dutch rider Kirsten Wild claimed the silver medal, with Amy Cure of Australia taking the bronze.
(Reporting by Philip O'Connor in Stockholm; Editing by Ken Ferris)
