Australia have claimed two quick wickets before tea to take charge on day two of the first Test.
Agar's debut haul of 98 was a world record from a number 11, helping Australia reach a first-innings total of 280.
Just before tea a dramatic pair of dismissals in quick succession piled the pressure on England to respond.
With his next ball Starc had Jonathan Trott in trouble, with umpire Aleem Dar's decision against lbw overturned by the third umpire after a review from the Aussies.
England now stand at 11-2 at tea, 54 runs behind their opponents ahead of the second day's final session.