Manager, Hakan Hayrettin made a few changes from Saturday's defeat at Maldon, with Junior Baker and Danny Bunce replacing Craig Pope and Lee Flynn at the back. Luke Marshall, Joe Sweeney and youngster Brian Moses also came into the starting line-up; Moses making his first senior start for the club.
Both sides struggled to get to grips in the early stages, with East Thurrock's Sam Collins getting the first shot on target just after ten minutes.
George Kamurasi added to his recent collection of one-on-one saves, as he stopped Kurt Smith midway through the half. It was an error by Baker which let Smith in, with his attempted pass back woefully short.
Smith fizzed an effort wide, before Joao Carlos had Blues' first effort on goal which failed to trouble Richard Wray in Rocks' goal.
Blues took the lead ten minutes before half time, as a cross from Marshall on the right touch line, took a deflection off Simon Peddie, leaving Wray stranded.
The goal gave Blues confidence to push forward, and they ended the half far stronger than their Premier Division opponents.
Moses' height was causing the visiting defence a few problems, with Sweeney going close with a low drive which came after a deep cross from Bunce, before Moses headed over from close range.
Jared Small was introduced for the injured Sweeney at the break, with Blues again looking threatening after the restart. Carlos beat the offside trap, coming from deep, but with the keeper rushing towards him, he tried to lob the keeper instead of laying the ball off to Moses.
Bunce sent in a cross from the left which Moses did well to connect with, forcing a good save from Wray, and Matt Hall did well to block a powerful effort from Small. How much he knew of it isn't sure, but he was in the right place at the right time to prevent a second Blues goal.
Small created a chance from nothing on the edge of the area, but his shot just went wide.
Both sides made their full quota of substitutions as the game petered out, but deep in injury time Carlos made great strides into the area from the left, and as his shot was saved, the ball hit Joe Keith and trickled into the goal.
Blues face a trip to Maldon & Tiptree in the Fourth Round, with the provisional date set as Tuesday 27th November.
Grays Athletic: George Kamurasi, David East (Jake Hall 90), Ryan Kirby, Junior Baker, Danny Bunce, Luke Marshall, Leon Lalite, Kenny Beaney, Joao Carls, Brian Moses (Tyrone Scarlett 80), Joe Sweeney (Jared Small 46)
Unused Subs: Dan Candy, Perry Tamburini