After registering a win in one hour and 28 minutes, Gauff and Routliffe will take on Italian hopes Sara Errani and Jasmine Paolini for the WTA 1000 title.
External Affairs Minister S Jaishankar on Friday received and warmly bid farewell to the Italian Ambassador to India, Vincenzo De Luca during a formal farewell call in Delhi.
The Chilean struck 23 forehand winners to register a 3-6, 7-5, 6-4 victory, spoiling Tsitsipas' hunt for a third successive semi-final appearance in Rome.
Djokovic, who was struck on the head by a bottle from a spectator's rucksack after defeating Corentin Moutet in his opening-round match on Friday, expressed concern about his performance against Chilean Alejandro Tabilo.