Few in the Aviation Stadium crowd would have given Cornet, who had lost her previous three meetings against Serena, much chance of denying the Williams sisters a first tour final against each other since 2009.
But the Frenchwoman was unbowed as she slugged it out from the baseline against the world number one.
"This is the biggest win of my career," Cornet said in a courtside interview. "I had to forget about Serena on the other side of the net and concentrate on my own game. I tried to play very deep and stay focused."
The first eight games went with serve before Williams scuffed a forehand long to give Cornet the first break of the match and the opportunity to serve for the first set.
The 24-year-old made no mistake when her moment came, leaping to play a baseline backhand winner down the line to claim the set, then punching the air as the crowd bellowed her name.
Cornet was energetic while Williams looked lacklustre as the 17-times grand slam singles champion committed a series of rudimentary blunders.
"I'm a wee bit embarrassed," Williams, 32, told reporters. "I don't think I have made that many errors in a match in I think at least three, maybe four years. Out of 10, I was like a minus 283.
"I started out extremely slow. I need to be able to play better than that if I want to be playing on the professional tour. Maybe I can go to amateurs," joked Williams after only her second defeat in 30 matches.
Her competitive fire did awaken after Cornet took a 2-0 second set lead. She let out prolonged roars with every winner as she surged to 3-2 ahead, the set now back on serve.
But Williams, playing her first tournament following a month out with a back injury, could not sustain that surge.
Cornet broke again for a 4-3 lead with a drilled forehand down the line past Williams, who was stranded at the net.
Serving to save the match at 5-3 down, Williams saved four match points to hold eventually.
Yet Cornet was undaunted and served out the match to love after Williams shanked a cross-court backhand long.
Cornet seemed overwhelmed, skipping in delight across the court, although she said she was calm at the last end change.
"I said 'OK you are a big girl you can do it'. I was trying to relax," she added.
Earlier, world number 44 Venus Williams made it five wins out of five against Wozniacki in an error-strewn encounter as six of the first nine games went against serve.
Wozniacki, 23, had been in scintillating form in Dubai, dismissing Wimbledon finalist Sabine Lisicki in the first round and not dropping a set thereafter, but Williams' ground strokes proved too potent.
The seven-times grand slam champion claimed the first set after a deep return forced Wozniacki into scuffing a forehand into the net.
Williams, 33, cranked up the pressure in the second set, racing into a 3-0 lead.
Wozniacki, who topped the year-ending rankings in 2010 and 2011 but has since reached only one grand slam quarter-final, put up little resistance, ceding the match with another forehand into the net.
Williams has yet to drop a set in Dubai, beating four higher-ranked opponents along the way including former French Open champion Ana Ivanovic.
"I feel like I've just gotten so much better since my first round to now, just feeling comfortable on the court, feeling comfortable when I'm behind, feeling comfortable when I'm in the lead," said Williams, who has struggled for form since she was diagnosed with an auto-immune disease in 2011.
"It reminds me a lot of when I first came on tour ... I feel like I'm learning lessons all over again."
WTA Dubai Championships semi-finals
Alize Cornet (France) beat 1-Serena Williams (U.S.) 6-4 6-4
Venus Williams (U.S.) beat 8-Caroline Wozniacki (Denmark) 6-3 6-2
WTA Rio de Janeiro Open quarter-finals
Nastassja Burnett (Italy) beat 3-Paula Ormaechea (Argentina) 5-7 6-2 7-5
Teliana Pereira (Brazil) beat Irina Begu (Romania) 6-4 6-4
1-Klara Zakopalova (Czech Republic) beat Katarzyna Piter (Poland) 6-4 6-0
5-Kurumi Nara (Japan) beat Lourdes Dominguez Lino (Spain) 7-6(5) 2-0 (Dominguez retired)
- Sports & Recreation
- Venus Williams
- Caroline Wozniacki
- Alize Cornet