The home side took the lead when a Molyneux free-kick was fizzed in and somehow crept into the corner past a diving Tommy Lee in the Chesterfield goal.
Molyneux then grabbed his second of the game after he followed up a missed Danny Webber penalty, giving Stanley a two goal lead.
Accrington were then reduced down to ten men as Peter Murphy received his marching orders for a second bookable offence as his wreckless challenge meant Dan Gardner was stretchered off, before Molyneux side footed home his third of the game.
Despite constant Spireites pressure in the second half, Ian Evatt could only pull one back in the final stages of the game.
Accrington started the brighter of the two teams in the early exchanges, as midfielder James Gray tested the Spireites backline with a teasing delivery, narrowly missing the far post.
Chesterfield did appear to have a golden opportunity to open the score-line in the third minute when some hesitant Stanley defending saw winger Gary Roberts nod round the keeper, but after Roberts lost his footing, there was no blue shirt to tap into an empty net.
The score-line was broken just one minute later though, as an Accrington free-kick struck by Molyneux somehow evaded everyone, including a helpless Lee in the Spireites goal to give Stanley the lead.
Molyneux nearly doubled both the score and his tally for the day when he was able to capitalise on a mix up in the heart of the Chesterfield defence, but he raced clear and dragged his shot wide of the goal.
The chances were coming thick and fast for both teams in the opening minutes, and Chesterfield had a chance to level shortly after falling behind. Roberts’ jinking run down the left resulted in his cross picking out forward Armand Gnanduillet, but the striker placed his effort wide of the target.
Stanley doubled their lead in controversial circumstances in the 9th minute, as referee Scott Mathieson ruled that Evatt had brought down William Henry Hatfield in the area, leaving Molyneux to follow up Danny Webber’s missed penalty and blast the ball in to an unguarded goal.
Chesterfield grew into the game as the tie reached the half way stage of the first period, but despite Richie Humphreys’ pin point delivery in to the box, Gnanduillet couldn’t direct his header on goal and drag the Spireites back into it.
Things could have got a lot worse for the Spireites on the half hour mark, as an incisive Stanley break away saw Gray sneak in behind the defence, but a splendid Lee save kept him at bay.
Chesterfield were handed a lifeline in the 31st minute, as a clumsy Murphy challenge on wide man Gardner left referee Mathieson with no choice but to issue Murphy a second yellow card, forcing Gardner into leaving the field on a stretcher.
The dismissal gave Chesterfield a fresh batch of confidence, and it nearly showed immediately as Ollie Banks found space at the back post, but his well struck half-volley went narrowly over.
Despite the constant Chesterfield waves of attack, Stanley increased their lead to three goals from some slack defending. A misplaced pass from Sam Morsy allowed Molyneux to bear down on goal and stroke by Lee for his hat-trick.
The Spireites began the second half on the front foot, as expected, with two tame headers from Gnanduillet and first half substitute Marc Richards testing Marcus Bettinelli in the Stanley goal.
Chesterfield continued to press and pin the home side in their own half, with crosses coming aplenty but appeared to be lacking any sort of cutting edge around the 18 yard area.
With the game entering the final 15 minutes Banks thought he had pulled a goal back for the visitors, but when his shot hit the back of the net, the linesman’s flag blocked Chesterfield’s proposed route back into the game.
Banks again thought he had reduced the deficit with ten minutes remaining, as when Evatt’s knockdown found the young attacker, his sweet volley drifted just wide of the post.
However the Spireites did get on the score sheet with five minutes of time remaining, when make shift striker Evatt’s swivel and shot following a defensive clearance found the back of the net.
Evatt nearly made it 3-2 moments later after he latched on to Roberts’ corner kick, but his header was somehow cleared by Stanley’s Adam Buxton underneath his own crossbar.
Substitute Jay O’shea also went close late on for the Spireites, but Chesterfield left the Store First Stadium empty handed as they fell to a 3-1 defeat.