Tendayi Darikwa's 31st-minute opener put Paul Cook's men in front, but Chesterfield were pegged back thanks to Matthew Dolan's penalty three minutes after the break.
Hartlepool's Andy Monkhouse saw red for a second bookable offence midway through the second half and the leaders failed to make the most of their numerical advantage.
Chesterfield are now two points clear of second-placed Oxford United, who went down 3-2 at home to Plymouth Argyle.
Caolan Lavery put the visitors ahead a minute after the break before Asa Hall levelled matters in the 65th minute.
Reuben Reid restored Plymouth's advantage from the penalty spot nine minutes from time and sealed the points five minutes later. A Curtis Nelson own goal gave Oxford late hope, but Chris Wilder's side were left to rue missing the chance to climb to the summit.
Scunthorpe United, who appointed Russ Wilcox as manager on a permanent basis on Christmas Eve, are third after a 2-2 draw at struggling Bury.
The visitors looked on course to clinch victory after goals in each half from Sam Winnall, who was dismissed in the 69th minute, immediately after claiming his second.
Bury, though, staged a dramatic comeback in the final 15 minutes, Chris Sedgwick pulling one back before Daniel Nardiello ensured a share of the spoils with a 90th-minute equaliser.
Ian Sharps' 85th-minute winner saw Burton Albion go fourth after beating managerless Northampton Town 1-0, while fifth-placed Newport County were victorious by the same margin at Wycombe Wanderers, Michael Flynn's 31st-minute strike proving the winner.
Rochdale sit in the final play-off spot after a comfortable 3-0 home win over Mansfield Town, a double from Scott Hogan sandwiching Matthew Lund's effort.
There were wins for Portsmouth, Southend United, Cheltenham Town and Morecambe against Dagenham and Redbridge, AFC Wimbledon, Exeter City and Fleetwood Town respectively, while the games between Torquay United and Bristol Rovers and Accrington Stanley and York City both ended in 1-1 draws.
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