The Romanian kept her hopes of regaining the world No.1 ranking alive with an efficient 7-5 7-5 win, although an occasionally off-balance Barty battled gamely before losing to a top-5 player for the first time this year.
Barty realised the enormity of her task against Halep, the owner of six titles on European clay, when the 27-year-old described her 6-0 6-0 third-round demolition of world No.46 Viktoria Kuzmova as the finest performance of her career.
But Tsitsipas went two breaks up in the decider and converted his fourth match point to make Nadal, who has fallen at the semi-final stage in his three clay-court tournaments this year, wait for a place in a 50th Masters showpiece.
The Slovakian was successful with just 37 per cent of her first serves and won just six points behind it across a dismal display. Halep then served out the opening stanza at love, concluding the set with a backhand crosscourt victor.
A tense opening set started with Halep blasting her way into Barty's service games with regularity.
"I think I played well today".
"To play semifinals here, it's a very good result for me coming after that disappointment in Fed Cup", Halep said. Maybe she was nervous before the match a little bit. "It was nice, 1st time we've hit together, and it was a really good level". "But I knew that I had to because I've played her twice before already and it was on hard court and then I didn't know what to expect today so I tried to stay as focused as I could", Osaka said.
In a rematch of the 2018 final, Kiki Bertens got her revenge on Petra Kvitova cruising past the Czech in the last match of the day 6-2, 6-3.
Stefanos Tsitsipas showed incredible spirit and skill to upset Rafael Nadal 6-4 2-6 6-3 at the Madrid Open and reach his second ATP Masters 1000 final.
Top-ranked Naomi Osaka reached the quarter-finals with a straights-set win over Aliaksandra Sasnovich and will next face Belinda Bencic, who dropped only two games in her victory over Kateryna Kozlova, while Sloane Stephens needed three sets to defeat Saisai Zheng.
Stephens will meet Petra Martic, who earned a second walkover in a row when her compatriot Donna Vekic retired in the third set of their match.