An avoided shot from Callum McGregor gave the guests a half-time lead, while a terrifying goof from goalkeeper Ben Siegrist brought about a tap-in for Giorgos Giakoumakis.
The striker snatched a late second objective, helping on a work from substitute Karamoko Dembele.
Joined squeezed courageously yet presented little danger in assault at Tannadice.
The success extends the Scottish Prevalence pioneers' run of unbeaten homegrown games to 30.
Celtic, who have lifted the cup a record multiple times, join Officers, Hearts and Hibernian in the last four - the initial time the Glasgow and Edinburgh clubs have all made it this far together.
Furthermore, with the Association Cup currently in the prize room and an important lead in the association, fans' contemplations will turn a possible fifth high pitch in six seasons.
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In the midst of the early buzzing about, Celtic forward Daizen Maeda brushed the top of the net from quite far out.
The advancement came on 12 minutes when McGregor ran on to a short corner and let fly from the edge of the punishment region. Nicky Clark put a leg out trying to impede, yet just prevailed with regards to redirecting the ball from Siegrist.
The objective took the stuffing out of the home side for some time, as did the deficiency of lively midfielder Ian Harkes to injury, yet a wild test from Reo Hatate on Kieran Freeman reignited Joined after 30 minutes.
Be that as it may, an expansion in animosity and work-rate didn't stem the progression of Celtic assaults and there was a snapshot of debate when the guests thought they had scored a subsequent objective.
Maeda pressed a shot in from short proximity however the ball had come his direction through the arm of Giakoumakis. It was anything but a purposeful activity from the Greek, with the changed rulebook accordingly recommending the objective ought to have stood.
Before long, McGregor sent a bubbling exertion only wide of the top corner and a turning Giakoumakis then, at that point, volleyed askew.
The hosts kept on joining admirably after the stretch, despite the fact that they were scattered by such a large number of wayward passes.
Exactly when it appeared as though Celtic had been knocked off their step, they were given a gift by Siegrist, who bumbled a cross from Maeda at the feet of Giakoumakis and the striker couldn't miss.
From there on, Ange Postecoglou's side figured out how to keep Joined under control without a lot of fight and tracked down a late objective when Dembele's diverted shot circled up pleasantly for Giakoumakis to prod home.Dundee Joined's Thomas Courts: "We adhered to the errand however most likely didn't work the goalkeeper enough and we didn't give our fans - who I believed were huge all through - anything to truly yell about and make a genuine round of it."
Celtic's Ange Postecoglou: "We didn't actually offer them any chances to get close to our objective. We scored three objectives from home and I thought we took care of the climate well. Away from home, a 3-0 win in a take out game is extensive."
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