Buffon, who has made who made his 150th appearance in his Champions League career, was on the losing side as Juve were beaten in the 2003 and 2015 finals.
“Two years ago everyone thought it was my last final – but you have to believe in your dreams,” said the 39-year-old.
With Juve already leading 2-0 from the first leg, goals from Mario Mandzukic and Dani Alves left Monaco needing four goals in 46 minutes to progress.
Kylian Mbappe’s second-half strike made no difference to the result, but did ended Buffon’s run of 10 hours of Champions League football without conceding.
