Negassa worked with compatriots Fayera Gemeda and Sintay Yinesu in the closing stages as they broke up the lead group.
In a sprint for the line, Negassa triumphed in 2:15:05, to breast the tape 63 seconds outside Kenyan Shadrack Kemboi’s course record.
“This is my first race in South Africa and I won, so I’m very happy,” Negassa said.
Gemeda took second position, just five seconds off the pace, and Yinesu was third in 2:15:22.
Xolisa Tyali, who led for more than half the race before settling into the pack, fought hard over the last few kilometres to end fourth in 2:16:03. He was the only South African athlete to finish among the top 10.
In the women’s race, Jepkosgei took advantage after South African Mapaseka Makhanya was hit by cramps with less than five kilometres remaining.
The Kenyan, who had been stuck in Nairobi for two days due to visa issues, only arrived in Johannesburg the day before the race.
She shook off her travel hiccups, however, to win in 2:36:04, breaking Makhanya’s course record by 62 seconds.
“I was aiming to run 2:34:00 but people were not pushing the pace, so I’m happy with my time,” Jepkosgei said.
“I was very tired when I got here but it was a nice race. I’ll be happy to come back to South Africa to race again.”
Makhanya, competing in only her second marathon, was satisfied with her performance as she improved her career record by half a minute to finish second in 2:36:36.
She took the lead in the dying stages before Jepkosgei fought back to snatch victory.
As with Tyali in the men’s event, Makhanya was the only South African woman to finish in the top 10 of the annual 42km race.
“It actually felt easy but I started cramping and I had to stop for a bit because I was cramping, and that’s when she went past,” Makhanya said.
“But it’s a personal best for me so I’m happy.”
National half-marathon champions Stephen Mokoka and Rene Kalmer, both preparing for international marathons, won the men’s and women’s 21km races.
Mokoka, who will turn out at the Shanghai Marathon in December, clocked 1:04:38 to edge countryman Elroy Gelant by one second in a sprint finish.
Kalmer, competing at the prestigious Berlin Marathon at the end of this month, was more than a minute ahead of Lebogang Phalula as she secured a comfortable victory in 1:15:02.
Desmond Mokgobu came out trumps in the men’s 10km race in 31:00 and fellow south African Keneilwe Sesing won the women’s event in 38:05.