Just as in her quarter-final against top seed Maria Sharapova, Safina looked down and out - physically and mentally - before turning the match on its head.
Dementieva had looked completely in control after overpowering Safina to take a closely-matched first set, largely thanks to a crucial break at 4-4.
Both players had looked comfortable slugging it out on the baseline but it was the seventh seed who showed more subtlety and variety around the court and Safina did not appear to have any answers.
Safina slipped to 0-2 in the second set and had to save five more break points to hold.
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Watch Safina save match point and go on to win
Even then, she was struggling to stay with Dementieva, who used her powerful forehand to good effect and opened up a 5-2 lead.
But that was the start of Safina's unlikely comeback, which saw her win 11 of the next 12 games - including saving a match-point on her serve at 4-5 - to go on to claim an unlikely three-set victory.
This is a real breakthrough for me
Dinara Safina
Dementieva did take the second set to a tie-break but once Safina had secured that, she did not look back and her opponent had no answer to her powerful groundstrokes in the decider.
"At 2-5 down, I knew I had to change my game completely," Safina said. "I think she got confused because I wasn't hitting the ball anymore like I did in the first set.
"I was saying to her: 'OK, you have to hit the winner."
Kuznetsova looked set for a battle of her own when she trailed Kanepi 4-2 in the first set and the Estonian led 40-0 in the next game as she served to go 5-2 up.
That was as good as it got for the unseeded 22-year-old, however, and, as mistakes crept into her game, Kuznetsova stepped up a gear.
A run of five out of the next six games saw the Russian take the first set and move clear in the second before she closed out her victory with a forehand winner.
It's going to be very tough match
Svetlana Kuznetsova
Kuznetsova will be expected to see off the volatile Safina in the last-four but the 2006 runner-up says she is expecting a tough test.
"I'm the favourite, but this is something I'm used to because I play most of the matches and I'm favourite, so I take it as it comes," said Kuznetsova.
"It's going to be very tough match. Dinara is playing very well on clay courts. She won in Berlin and she has won two matches here when she had match points against her.
"She has many lives, so I'll have to be careful."
Safina, the sister of two-time Grand Slam champion Marat Safin, feels her progress is down to her improving her fitness since the start of the year.
"This is a real breakthrough for me to reach my first Grand Slam semi-final," she said.
"I had many disappointing losses at the start of the year but I hung in there and promised myself I'd work harder. Now that patience and work is paying off.
"Everything is coming together. I'm stronger and keep my emotions under control."
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