Moore's side looked odds-on for relegation before their recent revival, which continued thanks to Brad Walker's 47th-minute penalty against Mansfield, who had Junior Brown dismissed on the hour.
Hartlepool remain bottom, but are now just one point adrift of safety after closing the gap between themselves and nearest rivals Cheltenham Town and Tranmere Rovers, who lost to Exeter City and Burton Albion respectively.
Burton maintained their five-point lead at the top with a 4-1 win at third-bottom Tranmere. The visitors led through goals from Damien McCrory and Lucas Akins, with Kayode Odejayi pulling one back before half-time.
Jimmy Floyd Hasselbaink's side wrapped up the points thanks to Abdenasser El Khayati and an Adam Dugdale own goal.
Shrewsbury Town kept up the pressure in second place with a 2-0 home success against Oxford United, Liam Lawrence netting a double, while 10-man Bury ran out 2-1 victors at home to Northampton Town thanks to an injury-time winner from Adam El-Abd.
Ricky Holmes had given Northampton the lead after 10 minutes before Joe Riley was sent off early in the second half. Kelvin Etuhu levelled for Bury after 66 minutes and El-Abd grabbed the late winner.
Southend United and Newport County claimed 0-0 draws against Cambridge United and Plymouth Argyle respectively.
York City looked on course for a valuable win in their battle to beat the drop at Accrington Stanley until Josh Windass struck a 90th-minute equaliser in a 2-2 draw.
AFC Wimbledon won 1-0 against Portsmouth, Exeter beat Cheltenham 2-1 and Dagenham and Redbridge defeated Stevenage 1-0. Carlisle United were held 1-1 at home by Morecambe.
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