Cheptegei clocked 31 minutes 40 seconds around the 10.2km-long course in the Danish city of Aarhus, he and Kiplimo pushing Kenya's double defending champion Geoffrey Kamworor into third (31:55).
"It is an awesome feeling winning here today. Since I missed it last time in 2017 I now reached my mission to return with the gold medal," Cheptegei said.
"It means a lot to me to be the first ever Ugandan to win this title. The course was very hard and difficult but I had a very strong preparation at home in Kampala where the terrain is very similar."
The women's race, over the same distance on the muddy course, was led almost from start to finish by Obiri, 2017 world champion over 5 000m, a distance in which she also won Olympic gold in Rio in 2016.
The 29-year-old Kenyan clocked 36:14, just two seconds ahead of Dera Dida, with another Ethiopian, Letensebet Gidey, in third a further 8sec adrift.