But Clarke Carlisle's stoppage-time goal gave the 10 men a point.
Burnley manager Brian Laws hailed the never-say-die attitude of his players.
He said: "I was probably the happier of the managers because with 10 men it was always going to be tough.
"To concede in that last period was tough on the players because I thought we were in control for large portions of the game. Having said that, neither goalkeeper really had a lot to do."
Edgar had been booked in the first period and saw red with 11 minutes left for a trip.