The Argentine gave the visitors the lead on 29 minutes, finishing low into the bottom left corner from inside the area after a brilliant Juventus team move.
It was 2-0 on 59 minutes again through Higuain, who got ahead of goalkeeper Danijel Subasic to poke home from close range after Dani Alves’ measured cross.
Juventus, who are yet to concede in over 600 minutes of Champions League football, will defend their two-goal lead in the second leg in Turin on Tuesday evening.
During a frantic opening period, the first clear chance fell to Monaco hotshot Kylian Mbappe, who could only head straight at Gianluigi Buffon when found unmarked by Nabil Dirar.
Mbappe came close again moments later, getting in between the Juventus centre-backs to poke Dirar’s superb cross towards the near post, but Buffon was there again to block well.
And Juventus were ahead in brilliant fashion just before the half-hour mark as Higuain finished off a fine team move.
Paulo Dybala started off the attack with a fine flick for Alves, who exchanged passes with Higuain, before a clever backheel from the Brazilian fell into the path of the striker 15 yards out.
Higuain made no mistake, stroking the ball into the bottom corner past Subasic for his first goal in a Champions League knockout tie away from home.
Radamel Falcao nearly equalised after the break, but saw his low effort from inside the area gratefully saved by Buffon, before Claudio Marchisio forced Subasic into a low save as Juventus broke into the penalty area.
But Juventus got their two-goal cushion just before the hour mark through Higuain again, sliding home from close range from Alves’ dinked cross over the defence after Monaco had lost the ball under pressure.
Monaco looked shell-shocked thereafter as Juventus sat in to keep their lead for the remainder of the game, and the French side came close only once more as Buffon tipped over Valere Germain’s header late on.