Asher-Smith clocked a time of 7.05 seconds to win ahead of Neita's 7.13 in Birmingham, having earlier broken her British record in the heats with 7.03.
Destiny Smith-Barnett of the United States was third in 7.15 with Jamaican sprinter Jackson fourth in 7.18.
Asher-Smith, who will sit out the European Indoor Championships in Istanbul next month, said she felt ready to move on from the 12 months in which she lost her grandmother before the world championships in Eugene and went on to finish fourth in the 100m and third in the 200m before a hamstring injury dashed Great Britain's relay chances.
"It was a really challenging year for me in 2022 but, and I know this sounds crazy, it was not really physical. It was more as a human being," the 27-year-old said.
"We're all humans, we all have the ups and downs of adult life and that's just it really. So all I'm hoping for now is easy - no major life events for like the next two years and that'll be great.
"But I'm happy and I'm just really excited for the outdoors. I'm really excited to go into training. I've got a few days off now then we're going to get ready for 100m and 200m."
Britain's Laura Muir fell well short in her bid to break the women's 1000m world record.
The Tokyo Olympic silver medallist over 1500m won the race with ease but her time of two minutes 34.53 seconds was almost four seconds off Maria Mutola's mark posted back in 1999.
Keely Hodgkinson set a British indoor record of 1:57.18 in the 800m with the Olympic 800m silver medallist at Tokyo lowering her own mark set a year ago as she showed fine form heading into the continental championships in Istanbul.
Grant Holloway blasted through the 60m hurdles field in a meeting record of 7.35 as the world outdoor sprint hurdles champion left US compatriot Daniel Roberts trailing in second.
