The Italian giants went into the second leg with a 2-0 advantage following their impressive victory in Monaco last week, and first-half goals from Mario Mandzukic and Dani Alves put the tie well and truly beyond the Ligue 1 leaders.
Juventus had won the first leg at France by 2 goals to nil and are in a comfortable position to qualify for the finals.
The Bianconeri quickly got into their stride and took the game to the visitors but squandered all the chances that came their way, with Higuain and Mandzukic being the chief culprits.
Dani Alves, who made both Juve's goals in the first leg, was again instrumental in the first goal.
Kylian Mbappe, 18 and one of the hottest properties in European football, has scored 18 goals in his last 20 competitive games, while the team features other risky players including resurgent Colombian forward Radamel Falcao.
The final is in Cardiff on June 3.
Tempers then flared when Monaco defender Kamil Glik appeared to stamp on forward Gonzalo Higuain, although the referee took no action against the Pole, leading to a bad-tempered final 20 minutes as Juve ran out comfortable 4-1 winners on aggregate.
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Southampton , on the other hand, battled to a goalless draw with Liverpool at Anfield in the Premier League on Sunday afternoon. The Gunners usually build up a head of steam at the end of the season and truly their top four hopes are on the line.
Despite Juve looking likely to book a final clash against Real Madrid - which leads Atletico Madrid 3-0 after their own first leg - Monaco right-back Djibril Sidibe said his side thinks it can overturn the two-goal deficit.
"I'd say the greatest difference between this Juventus and the one you saw in the final two years ago is inner belief", he said.
Monaco have reached the Champions League semis for the fourth time after 1993-94, 1997-98 and 2003-04.
Just before half-time, Juventus doubled their lead with a superb strike from Alves.
Juventus hasn't lost a game so far in Champions League play, winning eight of the 11 games it has played and drawing the other three. "I really enjoy coaching, it helps me relax and when it starts to cause me stress, I will stop".
'We leave here eliminated, but still with our heads held high, ' Mbappe said. They only allowed two goals during Group F play.
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