The SPL basement boys earned only their fourth league win of a wretched season, and their first since 17 November after second-half strikes from John Baird and Jim McAlister cancelled out Dougie Imrie's early opener.
Brown insisted the win gave his side hope of pulling off a remarkable escape act, although they remain 14 points adrift of safety.
"I'm delighted for the players after that," Brown said. "They gave me everything and that's all all I can ask for.
"They never looked like giving in even when we went down 1-0 in the first half and weren't playing all that well, so they deserved to get the win in the end.
"They showed what they're all about and to keep going the way they did speaks volumes for them. We need everyone pulling together which is what we got tonight.
"It's still going to be difficult to stay up but this will at least give us some hope for the rest of the season."