The fly-half fittingly drilled over a 40-metre penalty to finish with 15 points, having also supplied the creative spark for Michael Horak’s first-half try.
While Everitt was booting his side into the Premiership’s top four, Saracens were left kicking themselves after an error-strewn game they took an hour to get to grips with.
Glen Jackson appeared to have dug them out of a hole a minute from time when he landed his fourth penalty to go with his conversion of Hamish Mitchell’s late try.
But ultimately his side paid for failing to take some glaring chances and for Jackson’s inexplicable misses from close range before the break.
Both sides were short of a creative influence, with London Irish fly-half Riki Flutey absent and Saracens centre Thomas Castaignede having failed a Boxing Day fitness test.
Saracens were short of a destructive force, too, with Cobus Visagie replaced at tight-head by Ben Broster and they struggled to contain the Exiles’ ambitious all-round game and combative front five.
Tevita Vaikona made some early inroads on the wing but two Everitt penalties to one from Jackson in the first 10 minutes nudged Irish in front.
Everitt then created the opening try with a subtly-weighted kick threaded through the onrushing defenders with Horak collecting to score, before the fly-half added three points with a hurried drop-goal from 40 metres out.
Jackson hauled his side back within range with a second successful penalty but missed two ultimately costly shots at goal immediately before the interval.
They should have added more points with the ball in hand, too, with Vaikona and Alan Dickens both putting the visitors under pressure only to turn round 14-6 down.
Their frustration was increased immediately after half-time when they were penalised for pulling down a scrum and Everitt increased the Irish lead again.
And tempers boiled over in a furious 25-man scrap sparked by a clash between Ben Skirving and Delon Armitage that saw both sin-binned by referee Wayne Barnes.
Saracens appeared to have lost the plot – no more so than when Kevin Sorrell opted to duck into a group of defenders with the line beckoning and chances at a premium.
But the centre kept his composure 10 minutes from time as part of a superlative move that hauled his team back into the game.
Sorrell broke and linked with Paul Bailey, whose overhead pass put Vaikona close to the line and the former Bradford Bulls star kept the ball alive for replacement Mitchell to twist over, Jackson converting to leave Irish leading by a single point.
He appeared to have won the game with his 79th minute penalty but there was still time for Irish to set up camp at the other end of the field, where Armitage hit the bar with a drop-goal effort before Everitt applied the finishing touch.