Lautaro Martinez gave Inter Milan the lead early in the first half.
Buffon made his 1,100th professional appearances of a stellar career.
Ashley Young fouled Juan Cuadrado in the 18-yard-box as Cristiano Ronaldo restored parity for Juventus from the resulting penalty.
The Portuguese forward scored the second goal when he capitalised on a defensive mix up by Inter Milan defenders to give the visitors a first leg advantage.
“This is just the first leg, we haven’t achieved anything yet,” Juventus coach Andrea Pirlo told RAI Sport.
“What this does prove is that if we are fully concentrated, it becomes difficult for anyone against us.”
The second leg will take place in Turin on Tuesday, February 9.
Napoli and Atalanta will battle it out in the second semi-final on Wednesday.