Jackett finished ahead of Paul Ince of MK Dons, Norwich's Paul Lambert and Southampton's Alan Pardew.
Jones has inspired Cardiff to the brink of the Championship's top two as his team won 10 points from 12 available.
Newcastle manager Chris Hughton had won the Championship award for both August and September.
It is the fourth time Jones has won the divisional award as Cardiff boss.
The 53-year-old, the longest-serving manager in the Championship after replacing Lennie Lawrence at Cardiff in May 2005, also won the gong in August 2006, January 2008 and October 2008.
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