Irish fly-half Everitt hit six penalties and a conversion while opposite number Ludovic Mercier barely got a sniff of the goal-kicking action with just a sole penalty and conversion.
The defeat for Gloucester, their second in succession after Leicester last week, has hit the Cherry and Whites hard and they have slipped out of the title-chasing pack.
For London Irish though, the victory will be savoured as new coach Brian Smith continues to revitalise the previously inconsistent Exiles.
The home side kicked off in fine style, immediately putting Gloucester on the back foot, and young winger Delon Armitage was unlucky not to score in the opening minutes.
Unsurprisingly it was Everitt who was first on the scoreboard with a fourth minute penalty and the number 10 kept the momentum going with two more successful kicks, while Gloucester had to contend with the loss of influential forward Jake Boer.
The South African powerhouse limped off the field after just 15 minutes and the visitors will hope the problem is not serious – Boer having made only three league starts this season because of a painful toe injury.
Mercier clawed back three points but with Gloucester uncharacteristically losing their own line-out time and time again they paid the price.
Again Everitt was the executioner, slotting home another six points before the break and putting the Exiles 15-3 ahead.
Gloucester did not give up though and after the re-start upped the ante. A well-worked line-out catch and drive nearly put the west country outfit back in the reckoning, though their efforts again proved fruitless.
Everitt added his sixth penalty to increase London Irish’s advantage to 15 points until a lucky charge down from replacement Peter Richards on Everitt’s clearance produced the first try of the afternoon after 70 minutes.
With Mercier converting Gloucester looked like they were back in the thick of the action but instead home favourite Brian Strudwick had the final word when he broke loose from the scrum to power his way over the try line. Everitt duly converted to seal the deserved victory.