The result stretched County's unbeaten run of league matches to 39 with another solid display against a battling Killie outfit.
There was little in the way of clear-cut chances throughout the 90 minutes with both defences on top and a draw was probably a fair result.
County's best chance of the game fell to Marc Fitzpatrick in the first half but his goalbound effort was booted off the line by Killie defender James Fowler.
The visitors should have take the lead after the break when Rory McKenzie was through on goal but County goalkeeper Michael Fraser blocked with his feet.
After a patient build-up Iain Vigurs let fly from 25 yards but his effort just cleared Killie goalkeeper Kyle Letheren's left hand post.
At the other end a Liam Kelly shot from just inside the 18-yard box was blocked by Scott Boyd after Rory McKeown set up the chance after a good run down the left.
County had the first real opening in the 10th minute when Ross Tokely headed down a Vigurs corner and Alex Cooper, making his first league start, nodded the loose ball over the crossbar from eight yards.
Play swung from end to end but it was the home side who created the next best chance when Rocco Quinn whipped in an inviting cross in the 27th minute which Colin McMenamin just failed to make contact with right in front of goal.
Quinn was showing up well on the left hand side of the park and the former Celtic player was causing all sorts of problems to the Killie defence.
The home side enjoyed a sustained spell of pressure in the last few minutes of the first half.
The nearest they came to opening the scoring was when Killie's James Fowler was forced to boot the ball off the line after a Vigurs corner was missed by Letheren but Fitzpatrick failed to make the right connection on his shot from the edge of the six-yard box.
But Killie rallied in the dying seconds of the half and Fraser had to get down well to turn away a long range shot from Borja Perez.
Killie came flying out of the traps at the start of the second half and Danny Racchi crossed for Kelly, whose shot was deflected wide of target.
County won a free-kick on the edge of the 18-yard box but after Vigurs' effort was blocked Quinn fired a dipping shot over the bar.
The visitors were enjoying a lot of possession and they had shouts for a free-kick on the edge of the area turned down after Boyd appeared to trip McKenzie - but referee John Beaton saw nothing amiss.
Killie came close to breaking the deadlock in the 55th minute when a Racchi free-kick brushed the side netting.
County threatened a couple of minutes later when McMenamin ghosted in at the back post to head a Brittain free kick into the side netting.
McMenamin became the fifth County player to go into the referee's book in the 70th minute for a tackle of Manuel Pascali in what was a far from dirty match.
There were chances at either end as the game opened up. Vigurs just failed to reach an inswinging ball from Quinn at the far post, and Fraser saved with his legs at the other end of the park.