Both of Higuain's goals came from Dani Alves assists, with the Argentine hitman rounding off a breathtaking team move to open the scoring just before the half-hour mark and converting the second from close range after the break.
While the second leg in Turin next Tuesday will be no formality, Juventus have never lost a two-legged European tie to French opposition and so impressive were they at the Stade Louis II that it is hard to imagine Monaco recovering.
In contrast Monaco, having won their previous 13 matches at the Stade Louis II and been so thrilling going forward all campaign, could not find a way through the brilliant away defence.
They will now need something very special next week if they are to make it to a first Champions League final since 2004.
"We also wanted another clean sheet and we are delighted with the result."
Juventus coach Massimiliano Allegri raised eyebrows with his team selection as he ditched his favoured back four, bringing Andrea Barzagli into a three-man defence in an attempt to thwart Monaco's prolific attack.
The tactic worked, although the absence of the marauding left-back Benjamin Mendy from the home side also played into their hands.
====================
Monaco did grow into the game after a slow start and teen sensation Kylian Mbappe was first to test Gianluigi Buffon with a header from Nabil Dirar's ball that the veteran goalkeeper held easily.
In the 16th minute the same trio were involved again, Dirar surging down the right and delivering a teasing ball to the near post that Mbappe diverted towards goal, with Buffon saving superbly.
Buffon, playing his 149th European game at the age of 39, started his career before Mbappe was born. But he remains one of the world's best and shortly after he was there to turn the ball behind after Radamel Falcao met another Dirar delivery with a terrific leap.
Paulo Dybala was involved initially before Dani Alves, now nearly 34, surged into the box, holding off Kamil Glik and cutting the ball back for Higuain to sweep home.
Higuain bounded over the advertising hoardings and across the running track to celebrate with the away support, before Juve retreated to ensure they held their lead into the break.
Although Monaco had glimpses of goal after the restart, with Falcao firing straight at Buffon, they were also their own worst enemies.
But when Tiemoue Bakayoko was hustled off the ball by Dybala, Juventus seized their chance. Alves delivered a hanging ball from wide on the right and Higuain escaped the attentions of Glik to apply a first-time finish.
Buffon then intervened to stop Monaco getting a goal back, producing a majestic save in the last minute to tip over Valere Germain's header from a Joao Moutinho free-kick.
Disclaimer: No Business Standard Journalist was involved in creation of this content
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