After a first half stalemate, Austin grabbed the game by the scruff of the neck and turned it Leeds' way with a virtuoso midfield display that delighted manager McDermott and left Yeovil boss Gary Johnson wishing he had a player of that quality.
First Austin drove through a retreating defence and McCormack pulled the trigger from eight yards three minutes into the second half.
Nineteen minutes later Jamaican international Austin threaded the ball through for McCormack to fire past keeper Wayne Hennessey from 18 yards and take his goal tally for the season to eight.
McDermott said: "In the first half we were edgy and there was a tension around the place after our defeat at Huddersfield, but the fans stuck by us and we played some good stuff in the second half.
"Ross scored two fantastic goals and our captain really stepped up to the mark when we needed him, causing them lots of problems. He is the ultimate team man."
McDermott added: "It was a tough game and there was not much football played in the first half. In the Championship you have to grind it out at times and we did that. After the second goal we could have gone on to double our score but we are happy with a clean sheet.
"If we can be there or thereabouts at Christmas it will be interesting. We have some good young players who are learning all the time and we are close to where we want to be."
Johnson bemoaned his side's lack of killer instinct in front of goal.
He said: "We lived with the opposition for much of the time and didn't park the bus, but we need that killer instinct.
"All managers know who those players are and where they are but you need the finances to go out and get them.
"Austin and McCormack won the game for Leeds with their quality. We can't bring in ready-made Championship goal scorers but we don't cry over it.
"We just have to hope our boys learn and improve quickly. We lack experience but that is something we will gain all the time so hopefully we will have a great second half of the season.
"We showed we have a performance in us with our win over Nottingham Forest which followed a draw against Brighton, but Leeds' quality came to the fore."
Leeds lost wing-back Stephen Warnock, who hobbled off shortly before half-time and left the ground with his injured foot in plaster, but Lithuanian defender Marius Zaliukas left the bench and had a solid debut as his side kept their second clean sheet in their last three games.