A youthful Monaco team had breezed through the tournament with free-scoring performances but they met their match on home soil against the experienced and ruthless Serie A champions.
Right back Dani Alves raced into the box and back-heeled for Argentina striker Higuain to sweep home a clinical finish just before the half-hour mark.
The same two players combined again for the visitors' second goal on 59 minutes, Higuain tapping in from close range from an astute cross by the veteran Brazilian defender.
Monaco had their chances but kept bumping into the tightest defence in Europe's top club competition with just two goals conceded in this campaign.
Veteran goalkeeper Gianluigi Buffon played his part with a string of crucial saves, notably from a shot from Colombia striker Radamel Falcao and when he tipped a Valere Germain header over his bar in the closing stages.
"We approached the game the way we had to and did what he had to do," Buffon told reporters. "We do have an advantage but we also know Monaco have excellent players capable of scoring away. It's not over".
Juventus combined well in the opening stages and were the first on target with a low drive by Dani Alves straight at Monaco goalkeeper Danijel Subasic on 13 minutes.
Relying on their trademark counter-attacking style, the home side threatened when teenage forward Kylian Mbappe collected a Nabil Dirar cross and forced Buffon to show his class.
Buffon was made to work again, punching out a header from close range by Falcao.
Mbappe provided a symbol for Monaco's problems with the Juventus defence when he collapsed in the box after being stopped by rugged central defender Giorgio Chiellini just before halftime.
"They had two chances and scored two goals, we had many and scored none, that says it all", said the 18-year-old Mbappe, who had scored 18 goals from his last 18 competitive games, including three in the 6-3 aggregate win over Borussia Dortmund in the last eight.
Chiellini was lucky to stay on the pitch when he escaped with a yellow card for elbowing Falcao in the face in the second half.
The Italian champions, who advanced to the last four with a 3-0 aggregate win over Barcelona, are ideally placed to reach the final.
Real Madrid beat city rivals Atletico 3-0 in the first leg of the other semi-final on Tuesday.
Juventus, who won the European Cup in 1995 and 1996, have never been eliminated by a French team in 11 previous meetings in European club competitions.
Monaco, who are close to winning the Ligue 1 title, face a struggle to reach their second Champions League final after 2004, when they lost 3-0 to a Porto side coached by Jose Mourinho after a great run featuring wins over Real Madrid and Chelsea.
(Writing by Patrick Vignal in Paris, editing by Ed Osmond)
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