A mistake-ridden Inter performance had given Juve the advantage in the tie and crucial away goals in the first leg.
The Nerazzurri consequently spent much of the return leg in Turin attacking in search of the goals that would turn the tie on its head.
Impressive work by Juve's rearguard ensured they never arrived and only the reflexes of Samir Handanovic stopped Cristiano Ronaldo from sending the Bianconeri into a final with Atalanta or Napoli in more convincing fashion.
Achraf Hakimi was a constant threat down the right in the opening 45 minutes, and the game's first clear-cut chance came in the 25th minute after he was hacked down on the edge of the area by Alex Sandro.
Romelu Lukaku could not get telling contact on Christian Eriksen's free-kick but Inter's pressing continued to cause Juve problems, with the Bianconeri throwing their bodies in the way to prevent Gianluigi Buffon from being tested.
It wasn't until the 42nd minute that either goalkeeper was forced into a meaningful save, Handanovic using his legs to stop Ronaldo from squeaking an effort inside his near post.
Ronaldo was profligate in blazing high and wide just before the hour following a counter from Adrien Rabiot and Handanovic then prevented him from converting Weston McKennie's excellently placed pass with a close-range save.
The Portugal star was left looking to the heavens in disbelief after he weaved past two Inter defenders and into the area, only to see Handanovic get down to his right and turn away a fierce drive.
Hakimi lashed into the side-netting from a tight angle with better options available in the middle, his team-mates' reactions summing up a frustrating night for Inter.