The European champion kicked for home off the back straight and found enough gas to hold off her Kenyan rival when Sum attacked after the final bend, claiming her first major title in one minute 58.
“I dreamed about the gold medal at world championships all my life and now I have this medal,” the 27-year-old told reporters.
“It was a good race, not so fast, and I was ready from the beginning to the finish. I knew all girls can finish strong, so I decided to start it on the last 200m.
“I think from tomorrow on I will start preparing for the Olympic Games in Rio.”
Canada’s Melissa Bishop stayed with the leading pair on the last 100 metres and got just in front of Sum at the line to claim silver in 1.58.12.
“This is really a good world championships for myself and my team,” she said.
“The race was slow on the first 400m. I stayed relaxed and composed because anything can happen on the last round.
“It is what it is and I am very pleased with the result. I set a new Canadian record last night and came back tonight with a silver medal.”
Sum, who has dominated the event since winning the world title in Moscow two years ago, took bronze in 1.58.18, well short of the world leading time of 1.56.99 she ran in Paris in July.
The 27-year-old, cousin of 2007 men’s 800m world champion Alfred Yego, said she had not recovered properly from her semi-final run.
“I did not feel very well, I do not know exactly what was going on. I was just not responding well,” she said.
“It was a tactical race but the last 200 metres were very tough and the ladies were also pretty fast, I just tried to catch up.
“What I learned from these championships is that it does not matter if you are coming with the fastest time, you come as any other ordinary athlete and have to go through all those rounds. It was a good lesson.”
(Editing by Ed Osmond)