Argentine striker Higuain was set up by Dani Alves to open the scoring in the 29th minute and then converted an Alves cross just before the hour as Juve claimed a seemingly decisive victory in the semi-final first leg at the Stade Louis II.
The Italian champions have the final in Cardiff on June 3 in their sights, with a showdown against holders Real Madrid, Higuain's former side, looking probable.
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"The dream we have been pursuing since August has been to get to Cardiff and we are just one step away," said Higuain, who was applauded off by the home support in Monaco.
He now has 31 goals this season following his 90 million-euro ($98 million) transfer from Napoli, helping Juve close on a potential treble.
Higuain, who ended a seven-game run without scoring in the Champions League knockout stages, added: "We have not won anything yet, so we mustn't get carried away. I always kept calm. I knew everyone had faith in me and that hard work is always rewarded in the end."
Juventus were immense in all areas against a Monaco side who have lit up Europe this season with their brand of attacking football.
The hosts found the Juve defence to be impermeable, with Gianluigi Buffon majestic as ever in goal.
The 39-year-old, making his 149th European appearance, denied Kylian Mbappe and Radamel Falcao in the first half and produced a stunning fingertip stop from Valere Germain late on.
Juventus, who welcome Monaco to Turin for the second leg next Tuesday, have now gone over 10 hours without conceding in the Champions League and Buffon has kept clean sheets in all five matches in the knockout rounds.
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"In every game I want to show that I deserve to play at this level despite my age. I work hard every day for this. The day I quit, I want people to be sad about it," remarked Buffon, twice a beaten finalist in the Champions League. "We had the right approach. They are a fearsome team and the only way to beat them was playing the way we did."
Buffon also praised coach Massimiliano Allegri for his decision to bring Andrea Barzagli into a three-man defence, thwarting Monaco's attack and allowing Dani Alves to wreak havoc down the right.
"Gigi showed that he is still a great goalkeeper. He always does it in big games, and Higuain scored two lovely goals. But to get results everyone needs to work hard. You need to make sacrifices and track back and he did that too," said Allegri.
Juventus could wrap up a record sixth consecutive Serie A title this weekend, when they face city rivals Torino, while Lazio await in the Italian Cup final.
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To put their performance in the principality into context, Monaco had won their previous 13 home games and scored in 41 consecutive matches at the Stade Louis II since November 2015.
"They were more clinical than us — with two or three chances they scored and we couldn't put any of ours away. Buffon made some incredible saves," said Monaco coach Leonardo Jardim.
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