England, at tea on the second day of the first Test, were 11 for two in their second innings with Mitchell Starc on a hat-trick after removing Joe Root and Jonathan Trott with successive deliveries.
Earlier 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 98 -- the highest score by any Test No 11, surpassing Tino Best's 95 for the West Indies against England at Edgbaston last year.
This topped the previous last wicket record stand of 151 shared jointly by Brian Hastings and Richard Collinge for New Zealand against Pakistan at Auckland in 1972/73 and Azhar Mahmood and Mushtaq Ahmed for Pakistan against South Africa at Rawalpindi in 1997/98.
Australia resumed Thursday on 75 for four, a deficit of 140 runs, after an overcast first day where seamer Peter Siddle rocked England with five for 50.
But Thursday saw sunshine and blue skies which promised better batting conditions for Steven Smith, 38 not out overnight, and Hughes.
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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