Goals from Ian Hendon, Tresor Kandol and Richard Graham had put Barnet 3-1 up, but Ben Chorley's 69th-minute penalty and Dyer's last-gasp strike for Milton Keynes ensured the Bees had to settle for their third straight draw.
The Dons started brightly and the diving Clive Platt came within a whisker of heading in Paul Mitchell's centre from close range in the eighth minute, but the whipped cross flashed just past his head.
Dyer unleashed a fizzing 30-yard drive that flew just wide of Barnet goalkeeper Lee Harrison's post, before Kandol got the better of visiting defender Chorley at the other end but his rasping angled drive flew just wide of the far post.
Izale McLeod was denied by a close-range double save from Harrison after a poor defensive header from Bees skipper Hendon had gifted him the chance midway through the first half.
And after Liam Hatch had gone close with a low drive from the edge of the box that Dons keeper Adolfo Baines saved well at his near post, Hendon emphatically put Barnet ahead from the penalty spot in the 38th minute.
Hendon gave Baines no chance with a ferocious spot-kick into the top corner, after McLeod had been penalised for impeding Simon King following Nicky Bailey's free-kick.
The Dons equalised just five minutes later when Sean O'Hanlon - who had moments earlier had a header cleared off the line by Liam Hatch - opened his account for the club from close range.
Dean Lewington's dangerous cross was sliced across the face of goal by Hatch, leaving O'Hanlon to tuck home the loose ball from seven yards.
The Dons burst out of the blocks in the second half but Kandol's cool finish put the Bees 2-1 up on the counter in the 52nd minute.
Kandol latched onto Dean Sinclair's pass and skinned Dons defender Drissa Diallo before slotting past Baines.
And then, just five minutes later, Graham made it 3-1 when he drove Kandol's pull-back into the top corner from ten yards.
Kandol found himself one-on-one with Baines, but after rounding the Dons keeper found the angle was too tight, so he cleverly cut the ball back for Graham to fire home his first goal of the season.
Chorley's cool 69th-minute spot-kick pulled a goal back for the Dons, after Aaron Wilbraham had been brought down in the box by Hendon.
And Dyer made it 3-3 when he rammed in the rebound from close range after substitute Scott Taylor's shot had been saved by Harrison.