Anning initially showed little emotion after her hard-fought victory, before collecting a British flag and beginning a lap of honour at the Nanjing Cube.
Holmes, who had attempted to defend her position from Anning on the inside of the track at the start of the final lap, fell across the line as the Briton clinched victory by three one hundredths of a second.
“It feels amazing,” Anning told BBC Sport. “It wasn’t the cleanest race but the goal was to win and get my first individual title.
“I wasn’t sure [I’d won]. I thought I just got there but I needed to make sure I didn’t see a disqualification. It was just a sigh of relief.
“After what happened at the Europeans, to come here and win is just an amazing feeling.”
Anning’s triumph was the British team’s second gold of the championships, after Jeremiah Azu won the men’s 60m title on Friday.
Team-mate Amy Hunt, 22, ran 7.11 secs to place fifth in a women’s 60m final won by Swiss sprinter Mujinga Kambundji (7.04).
Elsewhere, Armand Duplantis won a third consecutive world indoor title in the men’s pole vault competition, while Jakob Ingebrigtsen won his first world indoor gold in the men’s 3,000m.