It was 2-0 when Harrop's shot was saved and the ball rebounded to Johnson who fired into the net with 34 minutes gone.
Barkhuizen scored his second goal of the night in the final minute of the half when Radlinger got a hand to his low shot but was unable to prevent it from crossing the line.
Neil said: "It was a good, positive performance to score three goals and get a clean sheet so it's really pleasing.
"It was a ballsy way that we set up but we felt it was the best way to win the game.
"Our first real bit of quality play led to the first goal and we upped the tempo from there.
"That's us taking seven points out of nine now. We took the goals well and we've got a clean sheet so it's really pleasing.
"This is the best position we've been in during the three years I've been here and arguably the best position the club's been in for a decade so what we should do is embrace it.
"If I had to single one player out tonight it would be Alan Browne, he was excellent, but it would be difficult to pick anybody out who didn't play well tonight. They were great.
Barnsley boss Gerhard Struber was not happy with the way his players performed.
He said: "Our performance was very disappointing. I think we started well and for five to 10 minutes we were good. Then we made some big mistakes.
"Before I came to the club, this was the norm. In the last few games, we have not had problems with big mistakes.
"It was a big crash in the first half for my team and we made big mistakes like an amateur player.
"When we have the aim to stay in the league, we cannot make mistakes like this. We have no big focus in some situations.
"There was not enough to pick up points. It was not my style and also not the style that we've shown."