The 19-year-old Agar came to the crease with Australia on 117 for nine and shared a test record last-wicket partnership of 163 with Phil Hughes.
Agar fell two runs short of his century when he was caught by Graeme Swann off Stuart Broad at deep mid-wicket.
The previous highest individual test score by a number 11 was West Indian Tino Best's 95 against England last year.
Left-arm spinner Agar had only played 10 first-class matches before being named in the Australia side for the first Ashes test. (Reporting by Ed Osmond, editing by Justin Palmer)