With Manchester United David Moyes in the crowd, Chesterfield took the lead when defender Liam Cooper headed in with 55 minutes gone.
Fleetwood thought their chance to take something had gone when Jeff Hughes hit a penalty over the bar, but Parkin scored his third in as many games with a minute left to secure a 1-1 draw.
Hartlepool's impressive upturn in form continued as they won 3-0 at third-placed Exeter.
Pools were torrid at the start of the season but are climbing the ladder at pace now.
Jack Compton was excellent for them on the south coast and set up goals for Jack Baldwin and Luke James before finding the net himself with an angled drive.
Oxford took advantage of Exeter's loss to move into the top three as they beat Northampton 2-0.
James Constable opened the scoring with 44 minutes gone and, with Danny Rose adding a penalty before the interval for good measure, United were home and dry.
Mansfield let a lead slip against Bristol Rovers, settling for a 1-1 draw at Field Mill.
Lee Stevenson put the Stags ahead but Alefe Santos equalised with six minutes left.
At the bottom, Accrington's hunt for a first league win goes on.
They led at AFC Wimbledon thanks to the well-travelled Kayode Odejayi but the on-loan striker was soon sent off.
The Dons capitalised on that too, equalising through Alan Bennett for a 1-1 draw.
There was a late goal at Burton Albion too, Billy Kee being sent off for the home side before Freddie Eastwood's last-gasp strike got Southend a 1-0 victory.
Morecambe secured a first-ever league win at Bury, 2-0, thanks to goals from Ryan Williams and Tony Diagne, while in the day's early kick-off, Plymouth and Portsmouth drew 1-1 in an all-south coast clash at Home Park.
Captain Conor Hourihane scored Plymouth's goal but Ged Wallace made Pompey's point before the half-time whistle.
Jamie Cureton scored his 250th career goal as his Cheltenham side won 2-1 at Dagenham.
The veteran opened things up (31) but Abu Ogogo levelled soon after. Keith Lowe would make sure Cureton's day was a memorable one, though.
Rochdale were comfortable 3-0 victors against Newport County, taking an early lead through Peter Vincenti.
Graham Cummins made it 2-0 and Bastien Hery made sure of the points.
In the day's other game, a brace from Paris Cowan-Hall helped Wycombe beat Torquay 3-2.
Adebayo Azeez opened up for the Gulls before Jo Kuffour equalised against his old club.
Krystian Pearce put United back in front but Cowan-Hall had the last word.