Matty Yates coolly rounded substitute keeper Jacques Heraghty on 32 minutes to score the only goal of the game at the Falkirk Stadium.
It was the Blues' fourth win and fourth clean sheet in a row and a first defeat of season for champions Queen's. And a win Farrell says was thoroughly deserved.
"We played with a courage and a bravery," he said.
"They're a very good side and I'm not buying into the fact that they've won the league so it's over for them.
"They were determined they wanted to keep the unbeaten run going - it was only them and Rangers that could do that - and we knew it was going to be tough.
"We knew that at a point Queen's Park would come at us. We had to defend properly and we did that; we were excellent."
It got Stranraer's post-split programme off to the perfect start as they chase a place in the promotion play-offs. Next up is a home match with Elgin on Tuesday.
Farrell said: "I've said all season that I trust this group of players. We know what our objective is.
"That's now four in a row, four clean sheets and we've become the first team this year to beat Queen's Park.
"We're not getting carried away, we've not achieved anything yet and have still got three massive games of football yet to play."