A controversial penalty in injury-time denied MK Dons an impressive point on the road at in-form Millwall.
Robbie Neilson made three changes for the visit to the capital, recalling Darren Potter, Reeves and Kieran Agard – Stuart O’Keefe, Harvey Barnes and Nicky Maynard made way.
After an early header over the top by Byron Webster, Reeves forced a save from Tom King courtesy of a long-distance low drive.
Another one of the incomers – Agard – threatened in behind but couldn’t reach Paul Downing’s long through-ball on 16 minutes.
The Dons had settled reasonably well but they fell behind midway through the first half when Gregory headed home a right-wing cross from close range.
Neilson’s men responded and a superb chest-down from Reeves set up Agard but he was thwarted by the Lions’ keeper inside the 18-yard box.
However, the Dons were more clinical on their next attack just three minutes later as Reeves fired a fine 20-yard drive into the bottom left-hand corner – the first goal the hosts have conceded in 10 outings too.
That brought the sides level and that’s the way it stayed for the remainder of what had been an evenly-contested first 45 minutes.
Former Millwall man Ed Upson forced the first save of the second half courtesy of a 25-yard drive before, at the other end, David Martin comfortably gathered an effort from Fred Onyedinma.
That was his last involvement as he was replaced by Steve Morison, who really should have done better after the ball had fallen to him 12 yards out.
King was again called into action to deny Upson from a 25-yard free-kick not long before the hour mark – at which point, the hosts began to enjoy their best spell including a header over from Morison.
Despite their territorial advantage, the Dons were limiting their hosts to next to nothing and holding firm when questions were asked.
Martin was up to the task on 79 minutes, superbly tipping Ben Thompson’s 25-yard effort wide of the target.
As the game entered the final 10 minutes, the Dons countered and a clever ball from Muirhead set away substitute Harvey Barnes but he was crowded out by Jed Wallace inside the box.
Fellow substitute Nicky Maynard forced a save from King before a crucial touch from George Baldock at the back post denied Aiden O’Brien as the men from MK1 maintained the 1-1 scoreline with just over five minutes remaining.
Dons’ final substitute – Dean Bowditch – was presented with a golden opportunity to put the men from MK1 ahead on 87 minutes but he couldn’t keep his header down from Maynard’s cross when well placed.
However, the Dons’ hearts were broken in injury-time when Lee Gregory scored from the spot after the referee adjudged that he had been brought down.
Starting XI: Martin; Downing, Walsh, Lewington (c); Baldock, Potter, Upson, Williams; Reeves (Maynard 74); Agard (Barnes 58), Muirhead (Bowditch 84).
Unused subs: Nicholls, Tilney, O’Keefe, Ngombo.
Goal: Reeves (30).
Bookings: Walsh, Martin, Lewington, Baldock.