The Romanian, last year’s losing finalist, needed treatment on her hand after the first set and slumped ??to a 7-5 6-1 loss against the world No 70.
During a subdued display, Halep managed only five winners, while Lucic-Baroni fired down 29 and completed victory with an ace. ??
The Croatian, who had also beat Halep at last year’s US Open, said: “It’s incredible, she’s just a great champion and I respect her so much. It’s such a huge win.”
She will next face home favourite Alize Cornet, who progressed with a 6-2 7-5 win over Alexandra Dulgheru.
“I wish at least three French people will cheer for me in that match,” said Lucic-Baroni.