Coun Ashton recieved 536 votes in the election, followed by Labour’s Joseph Pearson with 123, UKIP’s Don Ransome with 50 and Richard Thornalley standing on the Blue Revolution platform with 13.
The turnout was 26.6 per cent.
The result sees the Conservatives retain a majority of 16 councillors across the chamber while UKIP have six. The Independents and the newly-formed Bostonian Independent Group also have four seats each.
Committee seats will be re-allocated in accordance with the political proportionality calculation and information circulated in due course.
The Old Leake and Wrangle Ward by-election followed the resignation of Conservative Coun Maureen Dennis.
Coun Dennis had been ward councillor since 2003.
She also stepped down from Old Leake Parish Council where she had been a member since 1998.