Barker, 25, was the only rider to gain a lap on the group after a staggering effort with 15 laps to go.
It's the perfect way for the Welshwoman to celebrate St David's Day and it is Great Britain's first gold of the championships.
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It is Barker's second medal after she was part of the team pursuit outfit that won silver.
WATCH - Barker wins points gold at World Championships
"It felt surreal after gaining the lap. There were still 15 laps to go and I was completely gone," said Barker afterwards.
"I was relying on fact that everyone else was really close together and controlling each other,
"I had a conversation with my coach before over whether we would we be happy to say I had a good ride. I said, 'No I'd rather take some big risks'. That could either have put me in 15th or put me in a position to win."
It is the second time she has won the points world title after she was victorious in Hong Kong in 2017.
Jennifer Valente of the United States took silver and Norway's Anita Yvonne Stenberg finished third to take bronze.
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