Midfielder Arne Engels scored with a penalty in the 18th minute on Wednesday night before striker Adam Idah fired in a second in first-half added time for his fourth goal in three games.
Japan winger Daizen Maeda notched two goals in four minutes after the break and Engels produced a glorious fifth on 72 minutes before substitute Nicolas Kuhn completed the destruction.
The crushing win demonstrated Celtic's strength even though boss Brendan Rodgers was frustrated at failing to recruit a replacement for main striker Kyogo Furuhashi who moved to French club Rennes for a reported fee of $A20 million.
The match was postponed on January 25 due to storm damage at Celtic Park in Glasgow but there was nothing wrong with the Hoops team who increased their lead over Old Firm rivals Rangers and are heavy odds-on to retain their title for a fourth successive time.
It was a desperate night for Tony Docherty's Dundee, who lost 6-0 at home to Hearts at the weekend.
Celtic's expected early pressure was relentless.
Midfielder Reo Hatate and Portuguese winger Jota, who recently returned 18 months after leaving for spells in Saudi Arabia and then France, sent in crosses which were dealt with by Dundee keeper Trevor Carson.
The visitors had a couple of forays forward which offered some hope but that dissipated when Celtic took the lead.
Referee Colin Steven initially awarded a foul to Dundee when Mohamed Sylla tussled with Celtic defender Auston Trusty at a corner but was asked to check his pitchside monitor by VAR Alan Muir. After a long look Steven pointed to the spot with Engels firing low to Carson's right-hand side for the lead and his sixth penalty in the league this season.
Just before the break Dundee succumbed again, Carson saved an initial effort from Idah and then parried Jota's drive before the former Norwich striker fired high into the net from eight yards.
The second half was a straightforward drubbing.
Jota showed some trickery coming in from the left before his right-footed cross to the back post was headed in by the unmarked Maeda.
Then some entertaining play from Hatate and Jota ended with Engels sending Maeda down the right channel and his perfect lob from the edge of the box beat Carson and dipped under the bar.Â
The Dundee keeper was beaten again when Engels curled a wonderful shot from 25 yards in off the bar before Kuhn delightfully lifted a shot from the edge of the box into the far corner to complete a fine evening's work for the champions-elect.
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