The away side had taken the lead two minutes before half-time with a penalty courtesy of Kieran Agard.
The Dons will feel hard done by after being the better team for much of the game, which saw them denied by post, bar and a fine display by Robins keeper Lawrence Vigouroux.
The home side almost took the lead in the second minute, with a ball chipped into the box by Conor Thomas but George Williams was able to clear for the visitors.
In the 29th minute the Robins had a penalty claim of their own, Nicky Ajose went to the floor following a challenge from Williams but the referee waved play on.
Two minutes before the break Ben Reeves was brought down in the area by Charlie Colkett, Agard put the ball to the right, and although Vigouroux dived the right way was unable to get a hand to it.
Obika rescued a draw with virtually the last kick of the game when he raced clear and slotted home.
Report supplied by the Press Association.
Match ends, Swindon Town 1, MK Dons 1.
Second Half ends, Swindon Town 1, MK Dons 1.
Corner,  Swindon Town. Conceded by George Baldock.
Attempt missed. Ed Upson (MK Dons) right footed shot from the centre of the box misses to the right.
Dean Lewington (MK Dons) is shown the yellow card.
Bradley Barry (Swindon Town) wins a free kick in the attacking half.
Foul by Dean Lewington (MK Dons).
Charlie Colkett (Swindon Town) is shown the yellow card for a bad foul.
Foul by Charlie Colkett (Swindon Town).
George Baldock (MK Dons) wins a free kick in the defensive half.
Goal!  Swindon Town 1, MK Dons 1. Jonathan Obika (Swindon Town) right footed shot from the right side of the box to the bottom left corner.
Attempt missed. Ed Upson (MK Dons) right footed shot from the right side of the box is close, but misses to the left.
Substitution, MK Dons. Callum Brittain replaces Harvey Barnes.
Foul by Raphael Rossi Branco (Swindon Town).
Harvey Barnes (MK Dons) wins a free kick in the defensive half.
Corner,  Swindon Town. Conceded by Joe Walsh.
Attempt saved. Conor Thomas (Swindon Town) right footed shot from the centre of the box is saved in the centre of the goal.
Attempt missed. Nicky Ajose (Swindon Town) right footed shot from outside the box misses to the right.
Conor Thomas (Swindon Town) wins a free kick in the attacking half.
Foul by Harvey Barnes (MK Dons).
Nathan Thompson (Swindon Town) wins a free kick in the attacking half.
Foul by Robbie Muirhead (MK Dons).
Attempt missed. Jonathan Obika (Swindon Town) left footed shot from the left side of the box is close, but misses to the left.
Nathan Thompson (Swindon Town) wins a free kick in the attacking half.
Foul by Darren Potter (MK Dons).
Attempt missed. Jonathan Obika (Swindon Town) right footed shot from the centre of the box is too high.
Corner,  Swindon Town. Conceded by George B Williams.
Attempt blocked. Ben Gladwin (Swindon Town) right footed shot from outside the box is blocked.
Attempt missed. Ben Gladwin (Swindon Town) right footed shot from outside the box is too high.
Substitution, Swindon Town. Bradley Barry replaces Dion Conroy because of an injury.
Raphael Rossi Branco (Swindon Town) wins a free kick in the defensive half.
Foul by Robbie Muirhead (MK Dons).
Ed Upson (MK Dons) hits the bar with a right footed shot from outside the box.
Substitution, Swindon Town. James Brophy replaces Fankaty Dabo.
Attempt missed. Ed Upson (MK Dons) right footed shot from outside the box misses to the left.
Attempt missed. Jonathan Obika (Swindon Town) right footed shot from outside the box misses to the right.
Substitution, MK Dons. Robbie Muirhead replaces Kieran Agard.
Substitution, Swindon Town. Ben Gladwin replaces John Goddard.
Harvey Barnes (MK Dons) hits the left post with a right footed shot from the left side of the six yard box.
Substitution, MK Dons. Paul Downing replaces Ben Reeves.
Jonathan Obika's last-minute equaliser kept Swindon's League One survival hopes alive by securing draw with MK Dons.