Makarova, who is also through to the semi-finals of the women’s doubles with Elena Vesnina, was the more consistent player throughout and won 6-4 6-2 to finally emerge triumphant in her fifth slam quarter-final.
Azarenka lost to Serena Williams in the final for the past two years and will drop out of the top 20 as a result of this loss.
The former world No 1 had played by far her best tournament since returning from a persistent foot injury at Eastbourne in June.
But it had not been an easy journey and she was pushed all the way by 21-year-old qualifier Aleksandra Krunic in the previous round.
Makarova, on the other hand, went into the match having not dropped a set and upset seventh seed Eugenie Bouchard last time out.
It was a contest of fierce hitting but it was left-hander Makarova who recovered from a break down to edge the first set with a break of serve in the final game.
The Russian is the leading female player to be coached by a woman having worked with Evgenia Manyukova since 2007.
Azarenka put the pressure on early in the second set but Makarova resisted and then broke for 4-2, prompting Azarenka to destroy her racquet.
It did not help her cause, though, with Makarova ending the match on a run of four games in a row, clinching victory when Azarenka placed a forehand wide.
Makarova said: “Finally I am in the semi-finals. I had five chances and finally I’m here. It’s a great feeling.”
On being coached by Manyukova, Makarova said: “I just really enjoy to work with her. Eight years we are working together and it’s getting better and better.”
Caroline Wozniacki stayed on course for a second grand slam final appearance with a 6-0 6-1 rout of Sara Errani in the quarter-finals.
The 10th seed will be a big favourite to reach the final when she takes on unseeded Chinese player Peng Shuai in the last four.
The 24-year-old said: “It was a great match. It was really tricky conditions with the wind but I stayed aggressive and it really paid off today.
“The first game was very important. I was a little bit nervous but I served really well after that.
“To be in the semi-finals means so much to me.
“It’s been an up and down year but it’s an incredible feeling and it shows that hard work pays off,” she said.