The Bees scored in the 12th minute when Sam Saunders' free-kick crept into the bottom corner and they doubled the lead in the 59th minute when Saunders broke away to set up Toumani Diagouraga to score from 12 yards.
Chesterfield responded as Franck Moussa lashed in a shot from the edge of the box, but more poor defending allowed Clayton Donaldson to head a third in the 80th minute. Mark Allott signed the Spireites off in style by firing in from 25 yards, his first goal since November 2009, but it could not save the Spireites from a 24th league defeat.
"I think we played quite well and passed the ball but we have conceded three goals and that's how we have been this season. It's about keeping the ball out of your net and the three goals were very soft.
"They were really poor goals to conceed and that's been our downfall. Sometimes we are very soft and the three goals summed us up. We have got to work a lot harder as a team to try and keep a clean sheet and keep things tighter.
"We have been in and around the relegation zone throughout the season and we've never got out of that position."