The leaders played a man down for the majority after Sam Hird's 37th-minute dismissal, although led through a Marc Richards penalty four minutes after half-time.
Victory was beyond them though as Abu Ogogo equalised on the hour.
It meant the Spireites retained their lead of the division on goal difference only as Scunthorpe and Burton both won on Sunday.
Deon Burton and Dave Syers scored the Scunthorpe goals in a 2-0 win to ensure a miserable festive period for Oxford, who had began the day in the automatic promotion places.
Burton overcame promotion chasing Newport County 1-0 thanks to a Billy Kee goal 11 minutes from the end.
Rochdale climbed to fourth with goals from Scott Hogan and Graham Cummins in four second-half minutes.
Bury edged away from the drop zone with a 2-1 win over fellow strugglers York. The Shakers got off to a flying start through Anton Forrester and Nathan Cameron before Michael Coulson pulled one back 17 minutes from the end.
York are ahead of Torquay, who sit in the drop zone, on goal difference only as the Gulls lost 3-1 to Exeter.
Tom Nichols, David Wheeler and Alan Gow got the goals from Exeter with Karl Hawley getting Torquay's goal.
Last-placed Northampton drew 0-0 at Portsmouth to edge three points from safety.
Jonathan Franks hit an injury-time winner as Hartlepool beat Morecambe 2-1. Jack Sampson had equalised on 87 minutes after Jack Baldwin scored first.
Mansfield were also 2-1 winners away from home with Anthony Howell and Matt Rhead on target against Cheltenham. Sido Jombati grabbed an 86th-minute consolation for the hosts.
Southend remained sixth after a 1-1 draw at Accrington. Luke Prosser won the point after a Mark Phillips own goal.
Reuben Reid's 88th-minute equaliser earned Plymouth a 1-1 draw at AFC Winbledon, who had led through Michael Smith on 47 minutes.
Fleetwood's trip to Wycombe was postponed just before kick-off due to a frozen pitch.