Korir won the men's race in one hour 54 seconds, taking almost a minute off the previous best in the Welsh capital.
Compatriot Jepchumba, who ran most of the women's race alone at the front, clocked 1:08:14.
Welshman Dewi Griffiths was eighth in the men's race, setting a personal best of 1:03:26 in the process.
Ebbw Vale's Richie Powell won the men's wheelchair race in 1:02:44, with Gintare Gaigaliene winning the women's equivalent in 1:39:58.
The Kenyans dominated both elite races, though, with Korir followed home by countrymen Cyprian Kotut and Charles Mneria.
Jepchumba, meanwhile, beat compatriots Flomena Daniel and Lenah Jerotich.
Many runners tackled the course in fancy dress, and organisers said 51% were running the distance for the first time.
Inspiring tales from the Cardiff Half Marathon
Catch up with the action and stories from the Cardiff Half Marathon from our live text commentary and see some images from the race below.
Kenya's Shadrack Kibet Korir and Violah Jepchumba set new course records to win their respective races at the Cardiff Half Marathon.