Diego Costa, Oscar, Eden Hazard and Pedro goals gave Chelsea a final pre-season victory against Werder Bremen but defensive troubles will have worried manager Antonio Conte.
Goals from Oscar, Willian and Costa secured a 3-0 win over Crystal Palace. It will be Chelsea's first win under Hiddink and their first of the new year.
Youngsters Micah Hamilton and Oscar Bobb both scored fantastic goals as Manchester City won 3-2 at Crvena Zvezda to secure a 100% record in Champions League Group G.
He was the first Chelsea player to score a hat-trick in the competition since Brazilian playmaker Oscar against MK Dons in 2016, and the first Englishman since Lampard against Macclesfield in January 2007.
Chelsea responded well to falling behind, almost pulling level shortly after, only for Fabianski to pull off a great save to tip over a long-range effort from Oscar.
The Italian started the likes of Diego Costa and Oscar but had to wait until the 41st minute before his side opened the scoring, Traore bundling home a scrappy goal.
Oscar Gloukh levelled for the visitors in the second half. Hakan Calhanoglu sealed Inter's win from the spot after Lucas Gourna-Douath fouled Davide Frattesi in the area.