The Bees won their sixth game of the season on the road thanks to second-half goals from Neal Bishop and Michael Leary.
Despite being pretty much safe already, Stanley could still require one more point to be totally sure of League Two football next season.
Stanley have now lost 14 games at the Fraser Eagle Stadium this campaign - more than any other side in the division.
The 26-year-old former York City midfielder Bishop opened the scoring on 54 minutes when he headed home Adam Birchall's right-wing cross from close range.
And then fellow midfielder Leary, 25, sealed the victory eight minutes from time when he nodded home Jason Puncheon's corner.
Accrington have looked completely devoid of any confidence on home territory all season - and had their away form been as bad, they would surely be fighting hard at the bottom end.
Barnet had no fewer than 16 shots at goal in East Lancashire - and Paul Fairclough will be delighted as the season comes to a close.
Bishop's header was his first goal since December, a barren run which was finally ended after 28 appearances. And Leary's headed goal eight minutes from time was his first of the season.
Bishop took full advantage of some slack defending to leave Stanley keeper Kenny Arthur with no chance, while Leary secured victory with a clinical late finish.