Striker Heidar Helguson came off the bench to score an equaliser in the 89th minute while QPR were down to 10 men after Alejandro Faurlin had been taken off on a stretcher with Warnock having used his three substitutes.
The 1-1 draw means the teams meet again in a replay at Loftus Road on January 19, which allows suspended captain Joey Barton to serve another game of his three-match ban.
He will now be eligible to return against Wigan, missing just one more Premier League game against Newcastle next Sunday.
Warnock said: "All credit to the boys, they kept going and I am delighted to be in the hat, especially as it means captain Joey will be back for the Wigan game, which is more important really.
"People talk about did we want a replay, well yeah we did. At 1-0 down with 10 men and going into the last few minutes it's a great result for us. It could be the turning point of the season.
"You need a bit of luck in the FA Cup, all the big teams do. The early rounds in the FA Cup are the most difficult from what I've been involved with.
"It was a glue-pot of a pitch and we came out a lot more positive in the second half. We had a couple of great chances. If we had gone in front we would have won the game."
MK Dons took the lead through striker Dean Bowditch and looked the more enterprising side throughout.
Manager Karl Robinson, who is already in trouble with the Football Association after being sent off against Colchester for an altercation with the referee, believed the result was an injustice.
He felt QPR's equaliser was offside and also believed referee Michael Oliver should have awarded the Dons a penalty when QPR defender Clint Hill appeared to handle the ball in the first half, but he was delighted with his team's performance.
Robinson said: "I respect Neil Warnock and QPR immensely for playing a strong team like they did. We missed two gilt-edged chances but we play with freedom.
"We make mistakes and we are going to get things wrong, but if you keep believing and playing the game the right way you are going to get results. We deserved a victory and it is a little bit embarrassing that it has been taken away from us."
On the QPR goal he said: "Offside. I made a big mistake last week, I've apologised for it and I am going to be penalised.
"But there were two big decisions. There was a handball. I've never seen a player go to ground, put two hands above his head and then a penalty not be given. And the offside was an offside."
Meanwhile, Warnock confirmed he expected to bring in three reinforcements in the January transfer window before next Sunday's match against Newcastle.
Warnock said: "We are so short at the moment, we are looking to improve the squad. They were exhausted in the dressing room, you can't give any more than that. A lot of teams would feel sorry for themselves, but we are in the hat."
On the replay, Robinson added: "I can't wait. It's a London club I support. I watch them every now and then. I want to enjoy pitting our wits against a very good QPR team, but more importantly for me we have now got Carlisle at home.
"We've got a great team spirit and fantastic fans and hopefully we can go forward together. I want to get this club in the championship."
