Townsend strike one of the best I've ever seen - Milivojevic
Palace fell behind to Ilkay Gundogan's 27th-minute header but Jeffrey Schlupp found a swift response before Townsend left Ederson with no chance by launching a remarkable 30-yard volley into the top-right corner.
Milivojevic compounded City's problems with a 55th-minute penalty and, although Kevin De Bruyne's overhit cross flew in five minutes from time, the visitors held on to move six points clear of the relegation zone.
"The second goal was one of the best goals I've seen in my career – Andros' goal," said Milivojevic, before dismissing suggestions he might have seen a preview during training.
"No, this happened once!" he replied.
"Andros has that long-range shot and he used that. This goal today was amazing."
COME ON.#MANLIKESERBIA pic.twitter.com/ACDgyugStj
— Crystal Palace F.C. (@CPFC) December 22, 2018
Milivojevic saw a late penalty saved in a 0-0 draw against City almost 12 months ago and was delighted to hold his nerve on this occasion.
"The penalty was a massive goal for us because it gave them more pressure," the Serbia international added.
"I'm so happy. I'm proud of the team, proud of our fans."
The result leaves City four points behind Premier League leaders Liverpool after 17 games of their title defence.