Robbie Neilson’s side were twice pegged back after Stuart O’Keefe and George Williams had given the men from MK1 1-0 and 2-1 leads.
However, it was one of Saturday’s starters, Stuart O’Keefe, who handed the Dons the perfect start inside four minutes when his 20-yard shot deflected into the bottom corner.
Shortly afterwards, the men from MK1 almost made it 2-0 when Maynard turned and raced goalwards before shooting narrowly wide of the target – he had Muirhead in support but went alone.
Operating in the No.10 role, Harvey Barnes was looking lively as Robbie Neilson’s controlled the opening 20 minutes.
Against the run of play, Bradford were given a golden opportunity to level midway through the first half when referee Darren Deadman adjudged Joe Walsh to have committed a foul from a corner – Tony McMahon stepped up from the spot to level matters.
That gave the hosts a lift and signalled the start of their best spell, but the Dons countered and regained their lead on 35 minutes through George Williams, who found the net in off the post from a position closer to the touchline than the 18-yard box. Not sure how much he meant it but an incredible goal nonetheless!
The lead didn’t last for long, though, as Charlie Wyke headed home a right-wing corner to make it 2-2 three minutes before the break.
Lewington came close to restoring the Dons’ advantage in injury-time at the end of the first half when he flicked on the ball towards the back post but Colin Doyle managed to claw away the effort.
There were chances at either end in the opening five minutes of the second half – Barnes forced Doyle to tip an effort round the post before Alex Gilliead fired over the top.
Wyke and Billy Clarke then saw efforts blocked in quick succession before David Martin made a superb save to deny James Meredith after McMahon had pulled it back.
The Dons were still looking dangerous and George Baldock and Muirhead combined to pick out Maynard, who couldn’t get enough on a difficult cross.
Neilson made a double change with 25 minutes remaining as he introduced Chuks Aneke and Kieran Agard but it was Barnes who went closest next, forcing Doyle into a brilliant away after a quick break.
It didn’t take long for the two subs to get involved, though, as Aneke set up Agard from Barnes’ cross but he couldn’t find the bottom corner from inside the 18-yard area.
At the other end, Lewington was in the right place at the right time to clear away Meredith’s delivery as both sides continued to keep supporters on the edge of their seats in this end-to-end encounter.
An injury forced Aneke to be withdrawn with five minutes remaining – Darren Potter his replacement.
Potter & Co then defended strongly to hold on to a deserved point at a very difficult place – they even could have won it late on when they countered.
Starting XI: Martin; Downing, Walsh, Lewington (c); Baldock, O’Keefe, Upson, Williams; Barnes; Muirhead (Aneke 64 (Potter 85), Maynard (Agard 65).
Unused subs: Nicholls, Potter, Bowditch, Reeves, Ngombo.
Goals: O'Keefe (4), Williams (35)