The 19-year-old came home in 47.53sec, 0.19sec ahead of Italian Alessandro Miressi with Hungarian Nandor Nemeth third at 0.25.
It was a first individual medal at a world championship for Pan who should make his Olympic debut in Paris in July.
"I've prepared very well. I know this is just the beginning and I'm going to keep on working," he said during the poolside interview. "See you in Paris."
Pan set a new world record of 46.80 leading off as China won the freestyle relay on Sunday after a blazing first lap of 22.26. This time he was more conservative, turning in 22.55, but was still in first, just ahead of Miressi.
Pan said he had been "a little bit stressed" ahead of his first individual final of the competition.
"The time was not very good," he said.
In the evening's opening final Britain's Laura Stephens went to the front early in the women's 200 butterfly and won in 2min 07.35sec, holding off a late challenge from Denmark's Helena Rosendahl Bach who finished 0.09sec back.
Lana Pudar of Bosnia was third.
Claire Curzan won her second individual backstroke gold in Doha as she added the 50m title to her 100m crown.
The podium on Thursday was the same as in the 100m, the 19-year-old American winning the sprint in 27.43, out-touching Australian Iona Anderson by 0.02. Ingrid Wilm of Canada was third.
