The game turned on a 63rd minute decision that saw Jason Taylor red carded for a foul in the penalty area.
John Akinde netted the resulting spot-kick and sealed a first win of the season for Barnet on their return to the Football League although manager Martin Allen felt his side had played better in their earlier matches without any reward.
Cobblers boss Chris Wilder had warned after the win against Exeter that his team had not played particularly well and that caution was justified on Tuesday.
Northampton still lie 7th in League Two and will look to return to winning ways at home to Plymouth Argyle on Saturday afternoon.