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.
That pressure continued after the break with Juve surprisingly sluggish on the counter-attack in their bid to kill off the tie.
Monaco ultimately ran out of steam towards the end of a low-key second leg as Juve displayed typical defensive strength to stay on course for a domestic and continental treble.
The hosts were perhaps made to pay for a first half that saw them make most of the running, Kondogbia flashed a fierce drive wide in a purposeful start before testing Gianluigi Buffon again from range 19 minutes in.
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.
Arturo Vidal and Giorgio Chiellini clumsily sandwiched the Frenchman but Scottish referee William Collum waved away protests.
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.
Buffon redeemed himself to come out and save from Berbatov after Juve lost possession in overplaying at the back.
Juve gradually began to bring more composure to their game and kept hold of the ball well after the hour as they sought to see out the result and frustrate their hosts.
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.
But any late Monaco surge failed to materialise, keeping Juve on course to add European silverware to their domestic dominance.
