Australian team achieved a feat with a highest run rate in a test match innings against Pakistan in Sydney on 6 January 2017. They scored 241 for the loss of 2 wickets in 32 overs with a run rate of 7.53.
The previous teams who achieved this record were.
West Indies- 173/6 in Kingston on Feb 23 1983 against India
South Africa- 340/3 in Capetown on March 4 2005 against Zimbabwe.
West Indies-129/1 in Leeds on 8 June 1995 against England.
Pakistan-164/1 in Karachi on 14 November 1978 against India.