Axelsen will now face either Takahashi Koo from Japan or Loh Kean Yew from Singapore in Sunday's final in the Super 300 tournament.
Popov had won the most recent clash between the two when he shocked Axelsen at the European Championships last year.
And on Saturday, the lively Frenchman again managed to match Axelsen in many aspects of the game.
Thanks to his aggressive style of play, he stayed in the first set until the end before Axelsen wtih a creative serve swung the tide in his favour. .
In the break between first and second set, Viktor Axelsen had to take off his shoe to nurse a blister on one of his big toes.
Back on the court, Axelsen did not seem bothered by the toe, but he still struggled to dominate Popov in the same way that he did during the first set.
The prolific Dane showed signs of frustration several times, and he failed to get back into the set despite persistent attempts.
Axelsen had the brigtest start to the third set and showed for a while why he is the favorite every time he lines up.
Ahead 9-5 it looked like a clear Danish win, before Popov fought back towards the end of the match against Axelsen who used all his experience to finally book his ticket for tomorrows final.