The Dons fell to a 2-0 defeat at the hands of Bristol City on Saturday afternoon, but remain five points clear of the bottom three in the Sky Bet Championship.
Jay Emmanuel-Thomas replaced the suspended Samir Carruthers in the starting XI for the clash between the two automatically-promoted sides.
Both sides started the day on 31 points and there was nothing to separate the sides once the game had started, with neither able to create a clear-cut opportunity in the opening 15 minutes.
Lee Tomlin saw a shot blocked while, at the other end, Jake Forster-Caskey couldn’t quite pick out Rob Hall – both defences began on top.
Joe Bryan and Luke Freeman both fired long-range efforts off target for City as the midway point of the first half approached.
Murphy almost found Maynard on two occasions as the Dons enjoyed a spell of pressure as the game ticked towards the final five minutes of the first half.
However, the men from MK1 found themselves behind in injury-time when Tomlin latched on to a poor kick from David Martin and crossed for Kodjia, who finished from close range.
The Dons started the second half in a more positive manner and Emmanuel-Thomas fired a warning shot on 47 minutes.
Murphy then broke free down the left but couldn’t pick out a team-mate before Darren Potter drilled over the top after the ball fell to him on the edge of the box.
On a rare foray forward, Bryan fired just over the top from 25 yards, but Kodjia made it 2-0 on the hour mark when he beat the offside trap and superbly curled the ball past Martin.
Karl Robinson introduced Alex Revell, Dean Bowditch and Ben Reeves, the latter for his first outing since early January, to try and freshen things up and find a way back into the game.
Bristol City made substitutions of their own and Kieran Agard went close from 20 yards before Martin did well to thwart Freeman.
The Dons will be looking to bounce back against Huddersfield Town on Tuesday night.
MK Dons: Martin; Baldock, McFadzean, Walsh, Lewington (c); Potter, Forster-Caskey; Hall (Bowditch 61), Emmanuel-Thomas (Revell 61), Murphy (Reeves 70); Maynard.
Unused subs: Cropper, Kay, Spence, Williams.
Bookings: Potter, Murphy, Lewington.
Attendance: 12,825 (2,233 Bristol City fans).