The Romanian is yet to win a Grand Slam title but looks ominously ready to break her duck at Roland Garros.
Muguruza had hammered Maria Sharapova in the quarter-final but Halep was a different proposition entirely – and it seemed she knew it. A nervous start from Muguruza was immediately pounced upon by Halep for a break in the opening game.
Half an hour later 1-0 had become 6-1 and the challenge of Muguruza, who would have taken over at the top of the rankings with a victory, appeared to be fading fast.
She improved in the second set, breaking early on only to be pegged back at 4-4 before Halep held a marathon ninth game and broke for a 6-1 6-4 win.
American Sloane Stephens, the 10th seed, now stands between her and a first grand slam title.
It will be the 26-year-old Romanian’s fourth appearance in a major final, having also lost to Caroline Wozniacki in Australia in January.
But Halep feels better equipped to finally break her duck in Paris. She said: “I have more experience now.
“I feel calm. I feel that I have to enjoy it today, the victory, because it was a great match.
“Then I have two more days until I play the final. So I will stay chilled. I will relax. We will see what is going to happen Saturday, but for sure I will fight for every ball.”
Stephens beat her fellow American and great friend Madison Keys 6-4 6-4 in a repeat of last year’s US Open final.
That match was also won, comprehensively, by Stephens for her first grand slam crown.
This was a less clear-cut victory but an early break of serve in each set put Stephens in control.
Keys slipped two breaks down in the second but although she pulled one back Stephens served out for the match.
“It’s always hard to play someone from your country, and such a good friend, so I’m pleased to get through that,” said Stephens.
“It will be another great opportunity on Saturday and I’m really looking forward to it.”
The 12-time grand slam winner was stunned in the quarter-finals at Roland Garros by world number 72 Marco Cecchinato.
Italian Cecchinato won in four sets, scrambling over the line in an epic tie-break on his fourth match point.
Afterwards a dazed Djokovic, who has struggled with injury for much of the last year, was asked when he planned to make his first grass-court appearance.
He replied: “I don’t know. I don’t know if I’m going to play on grass. I don’t know. I don’t know what I’m going to do. I just came from the court. Sorry, guys, I can’t give you that answer. I cannot give you any answer.
“How do I regroup? I don’t know. I’m just not thinking about tennis at the moment.”
The Serbian needed lengthy treatment on a neck problem after dropping the first set.
But Cecchinato proved an even bigger pain in the neck for the 2016 Paris champion.
Djokovic had two set points at 6-5 in the second but went on to lose the tie-break.
Cecchinato was mixing things up to great effect, tying Djokovic to the baseline while throwing in regular, at times remarkable, spin-heavy drop-shots from the back of the court.
Yet Djokovic won the third set at a canter, and a suddenly frustrated Cecchinato was hit with a point penalty for unsportsmanlike conduct.
The storm seemed to have blown itself out and djokovic served for the fourth set at 5-3.
But from somewhere Cecchinato got a second wind, breaking back and forcing a tie-break.
It was a classic, Djokovic wasting three set points and Cecchinato unable to take the first of three for the match.
But on number four Djokovic left a looping backhand return which landed just in and Cecchinato celebrated a famous victory, 6-3 7-6 (7/4) 1-6 7/6 (13-11).
Cecchinato had not won a single grand slam match until he arrived at Roland Garros, but the 25-year-old is now the first Italian to reach the semi-final since Corrado Barazzutti 40 years ago.
He said: “Maybe I’m sleeping. It’s amazing. It’s unbelievable for me. For me to beat Djokovic in a quarter-final at Roland Garros it’s amazing.
“For me, it’s the first time semi-final grand slam. Now I need to think for the semi-final and I need some rest for recovery. I am very happy.”
— Roland-Garros (@rolandgarros) June 5, 2018
The 23-time Grand Slam champion revealed that she had suffered a pectoral muscle injury during her game against Julia Goerges.
“I unfortunately have been having some issues with my pec, my pec muscle, and (it) has unfortunately been getting worse to the point where right now I can’t actually serve. It’s kind of hard to play when I can’t physically serve,” Serena said.
The 36-year old did not answer whether she will compete at Wimbledon.
Serena Williams announces her withdrawal from #RG18 due to a right pectoral injury.
Wishing the three-time champion a speedy recovery. pic.twitter.com/bo3e1jkgcv
— Roland-Garros (@rolandgarros) June 4, 2018
“I’m beyond disappointed,” she said.
“I gave up so much time with my daughter and time with my family all for this moment. So it’s really difficult to be in this situation.”
Meanwhile, Sharapova said she was sad to see her opponent go out this way and wished her a quick recovery.
“I was looking forward to my match against Serena and am disappointed that she had to withdraw.”
“I wish her a speedy recovery and hope she returns to the tour soon.”