Left-winger Poole scored the winner - his eighth of the season - with half an hour remaining as the Bees' climb up the table continues under Scott.
The 35-year-old had been assistant to Terry Butcher, who was sacked in mid-December, and has impressed so much in his seven games in charge that he fully deserves the full-time role he has now been given - five wins, a draw and only one defeat is play-off form.
Scott has instilled confidence in his charges and they attacked from the off.
Chesterfield were sluggish, but luckily for them their goalkeeper was alert to the task.
Barry Roche was first called into action after 13 minutes when Alan Connell teed up Poole from Gary Smith's corner.
Through a packed box, Roche did well to dive down to Poole's drive.
Five minutes later and again from a corner, the keeper managed to push out Connell's header at the far post and then he tipped Smith's rasping shot around the post for another corner.
But Roche was finally beaten by midfielder Smith after Connell's pass dissected the defence to allow the 23-year-old to steal in and slot the ball under the keeper's despairing dive.
The goal shook Chesterfield to life and Jack Lester netted his 18th goal in only 23 games four minutes shy of the break.
The 32-year-old former Nottingham Forest striker swivelled and shot neatly past the onrushing Ben Hamer after latching onto David Niven's pass.
A exciting and flowing second half was played out and Poole's winner came about after the Bees had peppered Roche's goal.
The ball broke to the 26-year-old on the edge of the area and he showed excellent composure to steer his shot past the groping hand of the Chesterfield keeper.