When the former Kiwi opener reached 319 against Middlesex at Gloucester on Friday it beat the record of Grace who made 318 not out against Yorkshire at Cheltenham in 1876.
Spearman gave a clenched fist salute when reaching the milestone by clipping Ben Hutton off his legs for two.
The 31-year-old had already become only the third Gloucestershire player to make a triple century and the first since Wally Hammond in 1939.
Spearman went on to make 341, hitting 40 fours and six sixes, leading his side to 695 for nine declared in reply to Middlesex's 383.
The Kiwi, whose previous highest first-class score was 180 not out, played 19 Tests and 51 One-dayers for New Zealand between 1995 and 2001.
Spearman, who has a business-studies degree, retired from cricket in 2001 and planned to go into banking in London.
Fellow New Zealander John Bracewell, who was Gloucestershire coach at the time, asked him to play from time to time for the County and has become one of Gloucestershire's most consistent players.
He does not play as an overseas player as he holds a British passport due to his Welsh mother.