Former Arsenal and Fulham forward Luis Boa Morte made his Chesterfield debut as his side lost 2-1 to Dagenham at the Proact Stadium.
Boa Morte, who joined the club on Wednesday, made an impressive start by setting up an early chance for Neal Trotman.
But he was upstaged by Sam Williams, who scored twice to seal the win for Dagenham.
Barnet’s 4-1 home defeat to Plymouth leaves them seven points from safety and five behind second-bottom Aldershot, who were thumped 4-0 at leaders Gillingham.
Elsewhere Cheltenham went third with a 2-1 win at AFC Wimbledon, while Fleetwood dropped to fourth after losing 1-0 at home to struggling Wycombe.