Juve won the away first leg of the tie 2-0 on Wednesday courtesy of a goal in either half from striker Gonzalo Higuain.
But Buffon also played an important role, making five saves en route to a sixth consecutive Champions League clean sheet – a club record – and Allegri hailed the 39-year-old's performance at Stade Louis II.
100 - Gianluigi Buffon is only the 2nd Italian player to reach 100 #UCL appearances for the same team after Paolo Maldini. Captains.— OptaPaolo (@OptaPaolo) May 3, 2017
"Gigi Buffon's top performance almost goes without saying when it comes to these big matches," Allegri told the club's website.
"Gigi is the best goalkeeper in the world and he has shown that in this game. The best players step up to the plate on nights like this.
"Monaco are a good side, a technically gifted side, but we started well. It was beginning to look easy, but we made a few mistakes and Gigi produced a great save at 0-0.
"They created a couple of good chances after we took the lead, but Gigi was there to save again so there is plenty to be happy about.
"All of the defenders did very well – it is games like this that show just how good these players are."
Allegri stressed the job was not yet done ahead of next Tuesday's second leg in Turin, with Juve eyeing a second final in the space of three years.
"You have to hand it to the players, I congratulate them because it wasn't easy to come here to Monaco for the first leg," added the Juve head coach.
"That said, we still have to play the return leg and the job is not complete. They have nothing to lose so we will need to do a professional job once again.
"The lads are having a great season, but now we have the chance to make it an extraordinary one, so we must be focused."