The annual half marathon, Britain's biggest mass-participation run, saw Kipsang produce a scintillating sprint finish to beat fellow Kenyan Micah Kogo on the line with a time of 59 minutes six seconds.
Kipsang also won this year's London Marathon and took a bronze medal over the distance at the Olympics.
Three-times Olympic champion Dibaba, who was making her debut at the half-marathon distance, saw off the challenge of 2011 world marathon champion Edna Kiplagat to cross the line first in 67 minutes 35 seconds.
"It was a good race, the course was good for me on my first half marathon," Dibaba said.
"I enjoyed it. At the last minute we had rain but there is nothing you can do about that.
"Hopefully next time I can run a faster time and I am thinking of running a marathon next year."
Britain's 5,000m and 10,000m Olympic gold medallist Mo Farah did not take part in the race after deciding to rest following his summer feats but acted as one of the official starters as 55,000 people tackled the route from Newcastle to South Shields.