Jim Gannon handed Leslie Thompson his County debut as the Hatters looked to bounce back from Tuesday's defeat at Morecambe.
Adam Proudlock was the man to make way for the winger who moved to Edgeley Park on Thursday on a one-month loan from Bolton.
Keith Briggs also came in for James Smith who failed to shake off the ankle injury he picked up at Christie Park.
Paul Turnbull, outstanding in the reserves' midweek victory over Oldham Athletic was rewarded with a place on the bench.
Matty McNeil missed an absolute sitter in the 5th minute when the ball fell kindly to him from a clever Anthony Elding flick-on. Unfortunately though he couldn't execute the ball with any real power and the chance went begging.
Anthony Elding looked dangerous from the outset and he carved out a number of good chances as he carved the bees defence open.
Barnet took an undeserved lead on the 14th minute when Conrad Logan went to ground and pushed the ball to the feet of Adam Birchall who converted with ease.
County were almost back on level terms when Paul Tierney crossed to the head of Matty McNeil, but the Stockport Express Player of the Month's headed effort was punched to safety by Harrison.
Leslie Thompson was the next to go closest when he was fed a delightful ball by Adam Griffin, but his 18 yard shot went just over the bar.
County were back on level terms when Anthony Elding converted a spot kick, after Leslie Thompson was brought down in the box.
Elding went close again shortly before the break but his looping header was punched away by Harrison.
Both sides went in search of a second, but at the break it remained poised at 1-1.
County were 2-1 down, two minutes into the second half when Adam Birchall was again given the easiest opportunity to tap the ball in following more defensive lapses.
McNeil burst into the box on the 55th minute, but his effort was straight at Harrison and The Bees keeper was able to save with ease.
Thompson's trickery in and around the area, opened up a few chances for County as they went in desperate search of an equaliser.
It got worse for the Hatters when Nicholas Nicolau delivered a dangerous ball into the box and an unmarked Josh Wright was able to smash the ball home.
County went close when Adam Proudlock launched a powerful left wing shot, but the ball went just wide of the far post.
A good flick from Elding found the feet of McNeil but the big striker wasted another good chance as the game ebbed into the final exchanges.
The game was well and truly over when Ashley Carew scored a magnificent fourth.
Liam Dickinson narrowed the scoreline with a low drive in the final seconds, but the damage had already been done as County crashed to their first home defeat of the season.
