The talented centre-half popped up six minutes from time to cancel out Allan Smart's early penalty - just as it looked like the Spireites would be left to rue a host of missed chances.
The Dons got off to a bright start and went ahead in only the fifth minute through Smart's coolly taken penalty.
It was awarded after the pacey Wade Small intercepted Aaron Downes' horrendous back pass and was brought down by Chesterfield keeper Carl Muggleton as he tried to go round him.
Chesterfield responded well and could have equalised almost immediately, but Dons keeper Matt Baker saved well from Mark Allott before Evatt blazed over from just five yards.
At the other end, Milton Keynes centre-half Ben Chorley should have done better when he rose unmarked to head Nicky Rizzo's corner straight into the grateful arms of Muggleton.
For the remainder of the first half it was Chesterfield who posed the biggest goal-threat, with a gale-force wind behind them.
Downes and the lively Adam Smith both went close before the Dons' Dean Lewington cleared Wayne Allison's header off the line.
The Spireites did not ease off after the break and carved out two glorious opportunities for Allott and Evattm, which both went begging.
Allott's powerful strike from Smith's jinking run and cut-back was saved by the legs of Baker in the Dons goal, while Evatt's volley from Allott's teasing cross fizzed inches wide.
Just as it looked as though Milton Keynes were set to hang on for their third straight home league win, Evatt pounced with a predatory finish in the 83rd minute.
The former Derby defender capitalised on Rizzo's error to fire in off the post from 12 yards.
Small had a chance to snatch an unjust winner for the home side in the dying seconds, but his close-range effort was blocked by Muggleton.