Paul Cook's men looked set to claim their eighth win in 11 games this season after Liam Cooper gave them the lead in the 55th minute at Highbury, but substitute striker Parkin levelled in the 89th minute to earn the hosts a point.
The sides remain first and second in the division after sharing the spoils, while Oxford United took advantage of Exeter City's surprise 3-0 home loss to Hartlepool to climb into third.
Chris Wilder's side had no problem dealing with early-season strugglers Northampton Town, as goals from James Constable and Daniel Rose secured a 2-0 win at the Kassam Stadium.
Meanwhile, Morecambe moved into fourth place with a 2-0 win over Bury at the Globe Arena, while Rochdale's 3-0 victory over Newport County lifted them above Exeter into fifth.
Mansfield dropped to seventh in the table after Alfie Santos struck an 83rd minute leveller for Bristol Rovers to cancel out Lee Stevenson's first-half strike.
Elsewhere, Wycombe collected their fifth win of the campaign after coming from behind twice to beat Torquay at Adams Park.
Paris Cowan-Hall was Wycombe's hero as he struck twice in the second half to seal the three points with a 3-2 success.
Cheltenham picked up a much needed win against Dagenham and Redbridge to move them away from the bottom two, while Plymouth Argyle and Portsmouth battled out a 1-1 draw at Home Park in the day's early fixture.
Southend needed a last-gasp strike from Freddy Eastwood to secure a 1-0 win over Burton Albion - who had Billy Kee sent off - at the Pirelli Stadium.
Bottom-placed Accrington Stanley looked set to break their winless start to the season away at AFC Wimbledon but eventually had to settle for a point after Alan Bennett's late leveller
Kayode Odejayi struck his second goal for James Beattie's side in the 17th minute, but he was dismissed for violent conduct just before the break and Accrington could not hold on with 10 men.
Bennett's goal - his first of the season - came in the 86th minute of the match and leaves Accrington with just three points from their opening 11 matches.
