Sweden's Emma Johansson won a sprint finish to take the first 93.8 kilometre stage from Oundle to Northampton with Marianne Vos second and the 21-year-old third.
Barnes won the best young rider and best British rider jersey's for her third-place finish with the second stage seeing the peloton go from Hinckley to Bedford.
Barnes is riding for UnitedHealthcare during the Tour and is one of a host of Brits in action with double junior world champion Lucy Garner sixth in the opening stage.
Another UnitedHealthcare rider Sharon Laws leads the queen of the mountains classification while the remaining members of the Great Britain Cycling Team all finished in the bunch.
Emily Kay, Ciara Horne, Hayley Jones and Katie Archibald formed part of that with Amy Hill ending the stage eight minutes and 44 seconds back.
The second stage will see the peloton travel from Hinckley to Bedford and Barnes admitted she could have scarcely asked for a better start to the inaugural Women's Tour.
"I've been nervous since I knew we were coming to the race, so to get stage one out of the way is great," she said.
"I didn't expect to be in third place, so to do that and win two jerseys is great; it was one of my best-ever results.
"Now I have to decide which jersey I'm going to wear, which will be quite exciting. It feels great to win them both and the British one especially, that's pretty special.
"The roads in Northamptonshire were great and everyone was out there cheering; the crowds were absolutely amazing.
"I want to thank all the fans for coming out, putting up with the elements and supporting me; it was been fantastic."
- Sports & Recreation
- Marianne Vos