Fachie clocked a world record of 1:01.351 to win ahead of Spain's Jose Enrique Porto and Jose Antonio Villanueva 1:02.707 and Netherlands' Rinne Oost and Patrick Bos 1:03.052, who took silver and bronze respectively.
Storey then followed up her Individual Pursuit gold from Thursday with a second title.
That haul helped Great Britain to the top of the Cycling medal table, while there were also golds for China, Australia and Romania on the penultimate day of Track Cycling competition.
In the women's Individual C1-2-3 500m Time Trial, He Yin of China won gold. The C2 rider clocked a world record of 42.448, factored to 39.158.
Netherlands' Alyda Norbruis, also a C2 rider, finished in 42.466, factored to 39.174, to be edged into silver, while Jayme Paris of Australia set a C1 world record of 45.449, factored to 40.476, to take bronze.
Carol-Eduard Novak of Romania won the men's Individual C4 Pursuit in 4:42.000 after qualifying in a world record.
Czech Republic's Jiri Jezek was second in 4:45.232, with Jody Cundy of Britain third after overtaking Diego Duenas Gomez of Colombia in the medal ride-off.
The equivalent C5 event saw Australia's Michael Gallagher win gold in 4:35.297, with Britain's Jon-Allan Butterworth (4:39.586) second and China's Liu Xinyang (4:38.443) third.