The two that won this contest were both from the top drawer, particularly the match winning second.
The first half found both defences well on top and chances were few and far between to such an extent that Barnet did not have a single finishing effort on target.
County beat that by one and it produced the first goal.
For the first time in the match there was a defensive mix-up all starting with a fumbled attempt by recalled goalkeeper Lee Harrison.
When the ball ran loose to Matt Hamshaw on the edge of the box, he lifted a delightful chip over the out-of-position keeper and into the net.
Hamshaw's first goal at Meadow Lane was greeted with some relief and held out the promise of an improved second half.
Notts County should have taken a further grip on the game on 57 minutes when Phil Picken and Hamshaw combined delightfully down the right touchline and Hamshaw's pinpoint cross left Delroy Facey with a glorious headed opportunity at six yards, but his effort struck Joe Devera and was cleared.
But County did not have long to wait for the clincher.
On 62 minutes, Ben Fairclough was as up-ended just outside the penalty area and Jamie Clapham's beautifully placed free-kick flew into the top corner inside Harrison's left-hand upright.
Barnet could have reduced the arrears on 83 minutes but, following a corner, Devera headed over while a minute later Notts County almost added to their lead.
Richard Butcher, brought off the bench for his first appearance since the end of November, was fed by Hamshaw only to see his finishing effort blocked by Harrison.