Dan Jones, Jacob Blyth and Lewis Hardcastle all scored in the first half to stun the second place Red Dragons.
The Bluebirds are in the top half and after a season of struggle last time out they have made a big improvement this term.
Evatt accused his players of being wasteful last week but after six points in four day he was quick to shower his side with praise.
It was Barrow’s first win at the Racecourse in 66 years and Evatt said: “It was a fantastic performance.
“We were quickly able to highlight their weaknesses and we took advantage of that.
“From start to finish, from back to front, we were outstanding.
“The players are improving and progressing all the time. They are taking on board what is being asked of them.
“They have effort, they played with desire and their had commitment.”