Poland's Hurkacz, who beat Roger Federer on his way to the Wimbledon semi-finals in July, won 7-6 (7/4), 6-3.
Murray, now ranked at 113, swept to a convincing 6-3, 6-3 victory over Vasek Pospisil, his fifth win against the Canadian in six meetings.
The Scot, 34, won seven straight games en route to a 4-6, 6-3, 6-2 comeback victory in two hours and 24 minutes.
Moselle Open: France's Gilles Simon beats compatriot Richard Gasquet in ninth attempt; Kei Nishikori enters semi-finals
Gilles Simon finally managed to beat his fellow Frenchman Richard Gasquet at the ninth attempt with a 7-6 (7/4), 6-2, victory in the Metz quarter-finals on Friday.
Qualifier Peter Gojowczyk won his maiden ATP title at the Moselle Open in his first final, defeating seventh-seeded Benoit Paire 7-5, 6-2 Sunday.