Everitt's last-gasp strike earned his side a share of the points, but it will be scant consolidation to the Exiles who dominated the vast majority of this game.
Irish looked on course to consolidate their wildcard play-off aspirations with a win, but the visiting team almost snatched victory when Simon Keogh crashed over for a last-minute try.
Irish sorrows began early: they lost both their props – Rob Hardwick and Neil Hatley – to injury in the opening exchanges.
To their credit, the hosts managed to survive the blow, and went into the break with a useful 9-3 lead courtesy of three Everitt penalties to one from his opposite number Andy Dunne.
Quins took advantage of the Exiles' weakened pack in the second half by taking a maul up to the home line. Once within striking distance, Ben Willis peeled off the back and crashed over the try.
Dunne missed the conversion and then fluffed two penalties attempts, but the Irish found it hard to capitalise on the let-offs as their hooker Naka Drotske soon limped off the field, forcing the teams to play uncontested scrums.
The Exiles came close to scoring with skipper Ryan Strudwick and Flavin coming close, but in the end they had to settle for a late penalty.
The hosts looked home and dry, but Quins flanker Sanderson had other ideas: he flung out an excellent pass to set up Keogh on the right wing for his try.
Dunne made no mistake with the conversion to take the lead, but Everitt was on song and soon nudged over a penalty to scrape back two crucial Premiership points.
For London Irish:Pens: Everitt 5
For NEC HarlequinsTries: Willis, KeoghCon: DunnePen: Dunne