It seemed England would have a commanding first innings lead as Australia collapsed to 117 for nine in reply to the Ashes-holders' first innings 215.
But 19-year-old Agar went on to make the highest score by any Test No 11, surpassing Tino Best's 95 for the West Indies against England at Edgbaston last year.
Together with fellow left-hander Phil Hughes (81 not out), Agar shared a 10th wicket Test record partnership of 163 to take Australia to 280.
Left-arm paceman Mitchell Starc then followed up by taking two wickets in successive balls to leave England floundering at 11 for two.
But England captain Alastair Cook (37 not out) and Kevin Pietersen (35 not out) rebuilt the innings with an unbroken stand of 69 that left the hosts 80 for two at stumps -- a lead of 15 runs.
But the second day saw sunshine and blue skies which promised better batting conditions for Steven Smith, 38 not out overnight, and Hughes.
James Anderson, who on Wednesday had gone past England fast bowling great Fred Trueman's record of 307 Test wickets, made the breakthrough Thursday.
Smith, driving loosely at Anderson, gaining reverse-swing, was caught behind by wicket-keeper Matt Prior for 53. This was the start of an Australia collapse that saw five wickets lost for nine runs.
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