Heidar Helguson rescued a late draw for QPR to deny MK Dons a shock win - but the Premier League side's 11-year wait for an FA Cup victory goes on.
The Dons had a Jabo Ibehre effort ruled out for offside and a penalty shout for handball dismissed in the first half.
Dean Bowditch put them ahead as he finished coolly when Helguson failed to clear a Shaun Williams cross.
But QPR, who finished with 10 men after Alejandro Faurlin was injured, levelled when Helguson capitalised on a mix-up.
Karl Robinson's Dons have forged a reputation for being pleasing on the eye and they lived up to their billing in the first half, building slowly from the back and frustrating their Premier League opponents in front of their record crowd of 19,506.
Luke Chadwick and Ibehre had chances to beat QPR keeper Radek Cerny before Ibehre had an effort chalked off in a narrow offside decision.
All Rangers could muster in reply was a wayward Jamie Mackie effort and a DJ Campbell finish that was written off by the linesman's flag.
The Dons may have felt aggrieved when Daniel Powell's cross looked to clip Danny Gabbidon's hand as the defender went to ground in the area. Referee Michael Oliver waved away the calls for a penalty.
QPR looked like they were missing the influence of suspended captain Joey Barton but they started the second period with much more intent, driven on by the creativity of Federico Macheda.
Macheda, making his first start since joining on loan from Manchester United, almost found an opening when he jinked his way down the left and crossed for Campbell to nod agonisingly wide at the back post.
It had been the visitors' best chance and they were made to rue it moments later when MK Dons capitalised on a catalogue of defensive errors.
Williams collected Cerny's poor attempt to punch the ball clear and crossed to the back post, where Bowditch dispossessed the dallying Helguson before calmly slotting home.
It looked as if it would be plain sailing for the Dons, especially when QPR, having already used all three of their substitutes, saw stand-in skipper Faurlin carried off on a stretcher.
But Rangers dug in and were able to take the tie back to Loftus Road when Dons keeper David Martin got into a mess with his defenders and allowed the ball to slip to Helguson.
He made up for his part in the opening goal by rolling the ball into an empty net and, with it, ripped away Dons supporters' hopes of a memorable victory.
MK Dons boss Karl Robinson told BBC Three Counties Radio:
"What a class act. That's how football should be played. Not hoofing it and kicking it and playing off throw ins.
"I respect Neil Warnock and QPR immensely for playing a strong side.
"We missed some gilt edge chances and thought we deserved the victory. It was a little bit embarrassing it was taken away from us.
"Their goal was offside. And the handball - I've never seen a player go to ground with his hands above his head and a penalty not be given.
"But let's be proud of the players. I'm looking forward to having a drink with Neil Warnock and picking his brains about one or two things."