The Dragons were happy to return to form after struggling in recent games and losing confidence after going into administration - with a 10 point penalty imposed by the league.
Mark Jones provided the highlights of the afternoon with a superb 25-yard drive for his first league goal.
It put Wrexham in front and they never look back - although they survived a spell of pressure before making safe with their third goal.
Defender Stephen Roberts gave the home side a great start with an early goal, heading in after Jim Whitley nodded back across the box from Andy Holt's cross.
Chris Llewellyn was close to adding a second but Sammy Clingan took the ball off his toes as he was about to shoot. He missed his next chance, shooting wide over an open net.
Jones' unstoppable drive raised spirits as he finished superbly from Chris Armstrong's downward header outside the penalty area.
Armstrong nearly scored later when Dennis Lawrence headed back a cross goal from Darren Ferguson's free-kick only to be denied by Carl Muggleton who made a great save under the bar.
Mark Stallard was wide with a 25-yard shot earlier on, and when Clingan ran on to a pass from Mark Hudson with only the goalkeeper to beat, Andy Dibble raced off his line to narrow the angle and block the shot.
Stallard pulled a goal back on the stroke of half time, Hudson again making the chance.
Chesterfield tried to get back into the game with Clingan providing a left-wing cross only for Ian Evatt to head wide under pressure.
Wrexham sealed it just after the hour when Armstrong turned Ferguson's corner into the box for Llewellyn to smash it into the roof of the net.
Dibble pulled off a great double save to deny Chesterfield late on, parrying Stallard's shot and turning away Evatt's effort from the rebound.