Everitt created the game's opening try for Michael Horak and his kicking eased the Exiles into a 14-6 half-time lead.
A second-half clash between Ben Skirving and Delon Armitage sparked a 25-man brawl and saw both sin-binned.
Saracens fought back to take the lead through a Hamish Mitchell try and Glen Jackson's kicking but Everitt snatched the points for the visitors.
Saracens coach Steve Diamond:
"We didn't deserve to win on the strength of our first-half performance when our forwards took a hiding.
"We picked up in the second half but just couldn't quite turn it round.
"All credit to London Irish for taking the game to us and we couldn't get to grips with them for a while, but we let ourselves down with our execution."
Saracens: Scarbrough; Bailey, Castaignede, Johnston, Vaikona; Jackson, Bracken; Yates, Byrne, Broster; Raiwalui, Chesney; Vyvyan, B Russell, Skirving.
Replacements: Cairns, Mitchell, Seymour, Randell, Dickens, Bartholomeusz, BJ Russell.
London Irish: Horak, Armitage, Penney, Mordt, Bishop, Everitt, Hodgson, Hatley, Coetzee, Rautembach, Casey, Roche, Gustard, Danaher, Leguizamon.
Replacements:Wheatley, Russell, Strudwick, Murphy, Catt, Edwards, Laidlaw.
MMIX
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