Arturo Vidal's first-leg penalty proved crucial in the tie as Massimiliano Allegri's men booked an elusive semi-final berth, having fallen short at the quarters three times since their run to the final 12 years ago.
Allegri's men were made to work hard for their progression by a Monaco side that had shocked Arsenal in the previous round and conceded just twice at home in this season's competition.
Geoffrey Kondogbia went close twice before the break while Leonardo Jardim's side saw penalty appeals turned down when the midfielder went down in the box.
A series of fouls from both sides also punctuated play although Jardim's men should perhaps have had a penalty when Kondogbia appeared to be bundled over inside the area.
Carlos Tevez offered a reminder of Juve's threat with a shot narrowly wide from distance prior to the interval.
Throwing caution to the wind, Jardim introduced Dimitar Berbatov for Jeremy Toulalan at the interval and Monaco almost took the lead when Buffon flapped at a Joao Moutinho cross – though Patrice Evra was on hand to clear the loose ball.
Allegri's men could have wrapped up the tie in the dying embers when Andrea Pirlo's free-kick grazed the crossbar a minute from time.
