Jim Gannon made three changes from the side that won at Rochdale in midweek.
Chris Adamson came in for Conrad Logan after Leicester refused permission to allow the Irishman to play.
Michael Bowler replaced James Smith at right-back with Michael Raynes, back after illness, coming in for Anthony Pilkington who is still struggling with muscle soreness.
The first chance of the game fell to Liam Dickinson when the big striker's headed effort from a Tierney cross went marginally over.
Staines were putting every man behind the ball, making it very difficult for County to advance.
A quick reaction from Chris Adamson was County's saviour when Charles-Smith made the most of a defensive mix-up to find himself one on one with the County keeper.
County were struggling and when Clarke's long-range effort bounced off the far post and was then fumbled by Adamson it could have been even worse.
At the other end County won a free-kick following a foul on Elding. Dickinson took it, but it was well-saved by Allaway.
Matty McNeil had a golden chance for County on the 35th minute, when Griffin found him lurking at the far post but his headed effort went wide, much to the dismay of the restless County faithful.
Elding was the next to have a chance for The Hatters when he won the ball on the edge of the area, his weak shot however was never going to trouble Staines.
Michael Raynes attempt at a bicycle-kick minutes before the stroke of half time started to reek of desperation, as County started to run out of ideas and confidence.
Adam Griffin made an excellent burst into the box deep into injury time but the effort broke down, when neither Dickinson nor McNeil could supply the ammunition.
Staines, inevitably were the happiest at the break.
Second Half
Just two minutes into the second half and County were ahead when McNeil headed home at the far post following a corner ball from Tansey.
At the other end Owen had to be at his best to deny Staines a quick equaliser with a good defensive header.
Chris Adamson made a good low save to deny Staines, as the Middlesex side went in search of an equaliser to keep their cup dreams alive.
A burst from Dickinson nearly led to a second, but his lay off to Elding was poor and the talisman was made to work to keep the ball. In the end the danger was cleared by Allaway.
Staines went desperately close when Howard Newton had a chance blocked on the line by Adamson.
A mistake by Jason Taylor nearly resulted in an equaliser, resulting in a tongue lashing from Adamson. Moments later, Dickinson nearly found a way through at the other end with a long-range effort.
Staines were on equal terms though when, Marc Charles Smith found the net at close-range after Adamson had fumbled the ball following Howard Newton's long-range effort.
Matty McNeil's bursting run down the left flank with eleven minutes to go had County fans out of their seats. His cross was far too late though, and this was met with murmurs of discontent.
As the game entered the final exchanges, Dwaine Clark had an effort that just glanced the cross bar.
County will now have to do this the hard way-with a trip down to Staines. They wouldn't have wanted this at all.
