Matt Clarke had already grabbed a late equaliser on his 100th appearance to cancel out Ike Ugbo’s opener.
Luke McGee also made several fine saves, while Brett Pitman and Oli Hawkins both went close as it seemed as though the Blues were heading for defeat.
But Clarke’s header lifted a large travelling army and substitute Chaplin sent them delirious at the death.
Kenny Jackett made two changes from the side that drew with Doncaster on home soil the previous week.
Both were enforced, with the injured Stephen Henderson and suspended Christian Burgess making way for McGee and skipper Pitman.
It meant that striker Hawkins was once again forced into the central defensive role, where he has featured on many occasions this term.
Burgess was present at Stadium MK, however, sat with team-mate Stuart O’Keefe among the 6,257 away supporters.
The first half was an open affair, with the contest quickly switching from one end to the other, although it was the visitors who had more of the ball in the early stages.
Connor Ronan’s curling effort drew a save from Lee Nicholls, while the keeper also punched clear Matty Kennedy’s cross under pressure from Pitman.
Peter Pawlett’s drive was pushed away by McGee at the other end, but the first clear opportunity fell to Kieran Agard on 12 minutes.
The striker was slipped through on goal by Ed Upson, but was unable to keep his composure and shot wide of the post.
Pompey then threatened themselves when Gareth Evans picked up a loose ball and hit a fierce effort that Nicholls was just about able to parry behind.
Dion Donohue was next to force the stopper into action with a low drilled attempt after cutting along the edge of the box.
But it was MK Dons who broke the deadlock on 21 minutes, even if Ugbo almost managed to miss a simple chance.
Josh Tymon did well down the left and centred for Agard, who saw his effort saved at point-blank range by McGee.
Ugbo was left with an empty goal to fire into, however, and his shot clipped the inside of the post before nestling in the net.
Pompey tried to hit back and Kennedy’s sighter flew wide before a better effort from Ben Close swerved inches over the bar.
A brilliant effort from Pitman almost drew them level, only for a back-pedalling Nicholls to tip over the striker’s lob.
But the Blues might have found themselves further behind at the break, as McGee first saved Callum Brittain’s shot and then kept out a thumping Scott Wootton header from the resulting corner.
MK Dons 1
Jackett made a double substitution at the start of the second half, with Kennedy and Ronan withdrawn for Jamal Lowe and Chaplin.
Pitman thought he should have won a penalty when he went to ground under pressure from Dean Lewington, but referee John Brooks was not interested.
Chaplin then cut the ball back for Evans, who hit his shot cleanly enough, but the ball flew straight at a grateful Nicholls.
But the Blues were again indebted to McGee for a couple more fine pieces of goalkeeping around the hour mark.
Firstly, he used his feet to deny Ugbo and then, from the resulting corner, somehow managed to athletically tip over Upson’s header.
Again the action switched back down the other end and Pitman went it alone, bundling his way into a shooting position, only for a well-placed Wootton to hack the ball from the line.
The ball then fell for Lowe inside the area, but it bounced up at an awkward angle and forced the winger to fire over.
Pompey were struggling to break down their stubborn hosts, although they came close to levelling when Hawkins headed Donohue’s corner against the post.
Close then did well to steal possession and although his pass was too heavy for Pitman, the skipper managed to win a corner.
And it was from that set-piece that the Blues levelled on 84 minutes, as Evans played the ball to Donohue and his cross was headed home by CLARKE.
The visitors then survived a scare at the other end, as Upson’s free-kick somehow evaded everyone and flashed just past the post.
But it was the Blues who grabbed a last-gasp winner when Donohue’s cross deflected into CHAPLIN’s path and the striker swept the ball into the net.
MK Dons (3-5-1-1): Nicholls; Williams, Wootton, Lewington (c); Brittain, Pawlett (McGrandles 58), Upson, Cisse (Ebanks-Landell 80), Tymon; Ugbo; Agard
Goals: Ugbo 21
Subs not used: Sietsma, Nesbitt, Rasulo, Muirhead, Thomas-Asante
Pompey (4-2-3-1): McGee; Walkes, Hawkins, Clarke, Donohue; Thompson, Close; Evans, Ronan (Chaplin 46), Kennedy (Lowe 46); Pitman (c)
Goals: Clarke 84, Chaplin 90+3
Booked: Clarke, Thompson
Subs not used: Bass, Deslandes, Widdrington, May, Naismith
Referee: John Brooks
Attendance: 14,762 (6,257 Pompey fans)