Lying just one place above the bottom two, few expected James Beattie's team to get a result against a Chesterfield side that has spent the majority of the season in the top three, but they raced into a three-goal lead by half-time despite having a man sent off.
Molyneux scored twice in the opening nine minutes, but the hosts were then dealt a blow when Peter Murphy was dismissed just after the half hour.
Even with 10 men, Accrington grabbed a third before the break as Molyneux completed his treble, before Ian Evatt netted a late consolation for Chesterfield five minutes from time.
That result meant a win for Scunthorpe United would see them leapfrog Chesterfield to the top of the table, but Russ Wilcox's men also surprisingly dropped points as they were held 1-1 at home by second-bottom Northampton Town.
All looked to be going to plan for the hosts when Niall Canavan gave them the lead on 52 minutes and the visitors saw Ricky Ravenhill sent off six minutes later for a second bookable offence.
However, the 10 men of Northampton defied the odds to equalise through Zander Diamond in the 65th minute before holding on to extend their unbeaten run to four matches.
They moved a further point clear of Torquay United at the bottom, who lost 1-0 at home to Fleetwood Town thanks to Jamille Matt's 74th-minute winner.
That win moved Fleetwood up to fifth, sandwiched between Burton Albion and Oxford United, who met at the Kassam Stadium.
Burton came out on top 2-1 to move within two points of the automatic promotion slots after goals from Dominic Knowles and Zeli Ismail consigned Oxford to a third league defeat in four.
Elsewhere in the promotion race, Southend United and Plymouth Argyle both lost 2-1 away from home as they missed out on the opportunity make ground on those above them.
Phil Brown's Southend have been in torrid form since exiting the FA Cup to Hull City in January, and that slump continued at Morecambe as their winless league run extended to nine matches thanks to goals from Kevin Ellison and Jack Redshaw.
Plymouth, meanwhile, came into their game at Bristol Rovers on the back of three consecutive wins but failed to continue that run as Kaid Mohamed's 78th-minute goal won the day for the hosts after Neal Trotman had equalised Chris Beardsley's early opener for Rovers.
The league's form side York City continued their recent resurgence, Michael Coulson scoring the only goal of the game at AFC Wimbledon as Nigel Worthington's men made it five wins and two draws from their last seven outings.
Elsewhere, Mansfield Town beat Newport County 2-1 and Wycombe Wanderers defeated Hartlepool United by the same scoreline.
Eliot Richards' last-gasp goal earned Exeter City a point from a 2-2 draw with Dagenham and Redbridge, and Portsmouth's game with Cheltenham Town finished goalless.
