The Addicks had only won four npower Championship matches at home this season and looked short of confidence throughout, despite Danny Haynes coming close to equalising.
But it was Austin's brilliant strike from just outside the box that secured the points for Burnley to leave them eight points adrift of the top six.
And a delighted Dyche said: "I think that's the best result I've had as a young manager learning my trade.
"We had five senior players missing so to deliver that performance was terrific. I don't get too high with the highs or too low with the lows but we're a team that is improving in several ways.
"Like all of us on this difficult run, Charlie's been questioned a little but he's answered all of his critics. It was some goal."