Danny McSheffrey's side raced into a two goal lead before the interval thanks to goals from Kyle Rhodes on 23 minutes and Callum Woodward on 25 minutes.
The Leicester based side hit Sphinx with three goals in the space of five minutes just after the re-start. Gibbons hit the first in the 47th minute, followed by goals for Cooke in the 50th and 52nd minute.
James Holmes levelled for Sphinx in the 66th minute but five minutes from time and with Sphinx down to ten men, following the dismissal of Covsupport News Service sponsored Kyle Rhodes for two bookings, Cooke completed his hat-trick to snatch a win for Friar Lane.
On Saturday, Sphinx are at home to Castle Vale in the FA Cup.