Australia also saw off dangerman Kevin Pietersen in today's first session of the first Test and, at lunch on the third day, England were 157 for four in their second innings -- a lead of 92 runs.
Ian Bell was 20 not out and Jonny Bairstow unbeaten on 13.
The 19-year-old Agar transformed an Australia first innings on the brink of total embarrassment at 115 for nine yesterday with a stunning 98 -- the highest score by a Test match No 11.
After 19 overs, he had still to take a wicket but the Western Australia bowler put that right in his 20th.
Agar dismissed Cook for 50 after the left-handed opener, aiming leg side across the line of a delivery that landed in the rough and bounced, was excellently caught by Australia captain Michael Clarke, leaping high to his left at slip.
Cook's exit left England 131 for four as a tense capacity and sun-drenched crowd, watching for the most part in near silence, applauded politely.
