Giorgi, belying her ranking of 100th in the world, beat US Open champion Sloane Stephens in the first round and then ousted twice Wimbledon and former Sydney champion Petra Kvitova.
Kerber, who began previous year as No.1 before finishing at No.22, continued her 2018 resurgence with a thumping 6-3, 6-1 win over Slovakia Dominika Cibulkova.
Barty continued her strong buildup to next week's Australian Open in Melbourne, where she opens against World No 69 Aryna Sabalenka.
"I'm not looking back 2017 any more", said Kerber, who started to work with Wim Fissette obtaining immediate dividends. "Today it wasn't quite as good, but it was good enough to get the win".
"It's just the beginning of the year, so it's tough to say".
"We have set up a ideal platform for me to work with this year to try and go deep in tournaments, whether it's in Australia or in Europe or in the States".
"That has always been (the case) when I have been the No.1-ranked player".
Germany's Angelique Kerber won a seventh straight match as she steamed into the semifinals of the Sydney International on Thursday boosting her confidence for next week's Australian Open.
She will face Ashleigh Barty, who beat Australian compatriot Daria Gavrilova 3-6, 6-4, 6-2 in the other semifinal. "I think I shot myself in the foot with my serving in the first [set] and didn't give myself an opportunity to be dominant on service games", said Barty, who is now one win from becoming the first Australian woman to win the Sydney International since Alicia Molik in 2005.
"More than anything, I know what I can do and what I am capable of and how I can play".
Waiting for Del Potro in the last four will be Spaniard Ferrer, who brushed aside ATP NextGen Finals champion Chung Hyeon of South Korea 6-3, 6-2.
"I tried to play consistent and aggressive because with Chung, he plays with power, and it's never easy", Ferrer said in a court-side interview.
Ferrer's countryman Roberto Bautista Agut will play Dutchman Robin Haase in the other semifinal.
Italian fourth seed Fabio Fognini set up a semi-final against qualifier Daniil Medvedev following a 7-6 (7-4), 6-7 (7-4), 6-2 marathon against Frenchman Adrian Mannarino.
Death toll from California mudslides rises to 18
A search and rescue worker scours through properties after a mudslide in Montecito, California, on January 11, 2018. Authorities announced Thursday that 73-year-old Peter Fleurat was among those who died in Montecito.
NFL to look into whether Raiders violated 'Rooney Rule'
Back in 2003 the Lions were fined $200,000 for not interviewing a minority candidate for their head coaching position. The NFL seems set to investigate the Raiders hiring process to see if they violated the league's Rooney Rule.
Saif Ali Khan on why he refused 'Race 3'
Go to the page and see it before it disappears! The actor hasn't stopped impressing audience since the inception of his career. He, however, looked exasperated when someone pointed out that cuss-words in films leave a negative impact on children.