The Jamaican international scored the Whites' second goal at Elland Road to open his Championship account for the season and help United to a victory that sees them climb five places to ninth in the table.
Manager McDermott hailed the performance of his whole team, but withdrew Austin to a rapturous reception minutes from time so that the 28-year-old could be applauded for his outstanding display.
"The boys were really good," McDermott told reporters. "The international break came at a good point for us as it gave us a chance to work on things.
"Rudy Austin was excellent, as were all the lads, and I took him off for him to realise how much the Leeds fans appreciated his performance."
Leeds return to Championship action in the Yorkshire derby against Huddersfield Town next Saturday.