The Bees made just one change from the starting line-up against Burton Albion with John Oster coming in to central midfield at the expense of the injured Clovis Kamdjo.
From the first Edgar Davids and John Oster were seeing a lot of the ball and naturally they used it intelligently with the Gillingham midfield not being able to get to grips with the job in hand.
This was a below par performance from a side that is top of the table; but huge credit must go to the Bees because they simply refused to allow the home side the opportunity to muster any momentum.
In the first-half a cross from the left from Ricky Holmes almost produced an opener when Davids tried to back-heel the ball past Stuart Nelson, the Gillingham keeper.
But the Bees did take the lead when in the 19th minute Davids won possession on the half-way line and threaded a ball into the path of Hyde. There was still a lot to do.
Hyde then progressed goalwards and whilst still outside the box released a pile driver of a shot that thundered past the hapless Nelson.
Of course this prompted Gillingham to redouble their efforts to open their own account but poor approach play allied to sound defending meant that more often than not their attacks petered out.
With half-time approaching Matt Fish had a chance for the Gills, but the full-back up in attack was foiled by the impressive Graham Stack.
In the second-half the Bees had several chances to extend their lead; notably when Davids set up Andy Yiadom at the near-post.
David Stephens then had a headed opportunity but his effort went over and the fear was that by not taking one of these opportunities the Gills would draw level.
Midway through the half the Gills made a triple substitution and this gave the home side a boost; although it was short lived.
Adam Burchill, Deon Burton and Joe Martin had efforts on goal but Stack was equal to anything thrown at him.
In the final moments the Gills did put the Bees under pressure, but they lacked guile and looked unlikely to make any inroads.
This display was in marked contrast to the last away performance against Dagenham & Redbridge and there can be no doubt that the result was the right one with Barnet unquestionably worthy of the three points.
The Bees are away at Exeter City on Saturday.