Roy O'Donovan and Luke Guttridge hit the second-half goals to sink Edgar Davids' team who needed a final day victory to ensure League Two survival.
Barnet made a cautious start and Cobblers had two early chances with Ben Harding involved in both. The midfielder fired over before releasing Jake Robinson, who burst clear but saw Graham Stack save his weak effort.
O'Donovan was also thwarted by Stack after Mark Byrne fired Barnet's best early opening into the side-netting after neat play from Jake Hyde.
In a first half of few chances, Barnet should have broken the deadlock when Keanu Marsh-Brown beat the offside trap but shot straight at Lee Nicholls with the unmarked Luke Gambin better placed to score.
Byrne tested Nicholls with a free-kick although neither goalkeeper was seriously troubled in the first period.
Showing more urgency, Barnet twice went close in quick succession after the restart. Elliot Johnson's cross came back off the bar and Hyde's rebound was cleared off the line by Lee Collins.
But O'Donovan finally broke the deadlock in the 67th minute when he latched on to Guttridge's defence-splitting pass to beat Stack from 15 yards.
And six minutes later Guttridge doubled Northampton's advantage when he fired an angled drive past Stack after being set-up by substitute Adebayo Akinfenwa.
Barnet rallied but failed to create a serious opening that could have got them back into the contest as they saw their hopes of avoiding the drop disappear.