The early departure of starting fly-half Mark Mapletoft from the field saw Everitt brought on as a replacement, and the Irishman held his nerve by slotting two second-half penalties and a drop-goal to seal the points.
The Exiles had actually trailed 10-7 at the break, with a Paul Sackey try – converted by Mapletoft – after only two minutes being their only score of the opening half.
Gloucester scored all of their points in the first half, with Samoan flanker Junior Paramore crossing the line after 26 minutes – Henry Paul adding a conversion and a penalty.
But the Cherry and Whites could not get their game together in the second half, although Nigel Melville's men did at least claim a bonus point.
For London Irish:Try: SackeyCon: MapletoftPens: Everitt 2DG: Everitt
For Gloucester:Try: ParamoreCon: PaulPen: Paul