The hosts raced into an early lead through Emre Can's penalty inside seven minutes, after Jamie Bynoe-Gittens had been brought down by Kasper Schmeichel.
Celtic did however respond within just two minutes through Daizen Maeda's header from just six yards out, with the Japanese international rising high to meet Arne Engels's superb cross from the right.
Yet, the Scottish champions then proceeded to fall apart once Karim Adeyemi grabbed the first of his three goals, when in the 11th minute he raced on to Julian Brandt's through ball and fired a deflected shot beyond Schmeichel.
If there was an element of luck with Adeyemi's first goal, there was certainly nothing fortuitous about his second; the German international picked up the ball on a tight angle from just inside the box, and on his potent left foot he fizzed a ferocious drive beyond Schmeichel at his near post to make it 3-1 in the 29th minute.
Dortmund then added a fourth goal on 40 minutes through Serhou Guirassy's clinical penalty, after Adeyemi was clipped by Engels inside the box - and with that penalty Celtic had conceded as many goals in one half of football as they had in their opening nine games of the season.
There was however still time for another first half goal and for Adeyemi to grab his hat-trick, as the forward dispossessed Maeda on the edge of the Celtic box before unleashing an accurate strike into the bottom corner to make it 5-1 in the 42nd minute.
The hosts added a sixth goal in the 66th minute when Guirassy dribbled beyond Liam Scales with some delightful footwork, before sliding the ball beyond Schmeichel at his near post.
Felix Nmecha then made it 7-1 to Dortmund in the 79th minute, when after Celtic failed to clear their lines, the midfielder pounced on a loose ball and drove an accurate low strike into the far corner.
The hosts then finally relented as they saw the game out in the latter minutes, with Celtic fans no doubt having flashbacks to the 7-1 defeat they suffered at the hands of Paris Saint-Germain back in 2017.
BORUSSIA DORTMUND VS. CELTIC HIGHLIGHTS
7th min: Borussia Dortmund 1-0 Celtic (Emre Can)
Bynoe-Gittens beats Celtic's offside trap and as he races towards goal, Schmeichel mistimes his attempt to win the ball and brings down the English winger for a penalty.
Can steps up and opens the scoring for the hosts with a clinical penalty to the goalkeeper's right.
Daizen Maeda goal vs. Borussia Dortmund (9th min, Borussia Dortmund 1-1 Celtic)
After some patient and neat play down the right flank, Celtic have managed to respond in double-quick time through Maeda, who rises high to head home Engels's cross from just inside the six yard box.
Dortmund will be disappointed with the lack of pressure on the ball and how Maeda was able to head home unchallenged from so close in.
Karim Adeyemi goal vs. Celtic (9th min, Borussia Dortmund 2-1 Celtic)
It is raining goals in Germany, as Borussia Dortmund retake the lead courtesy of Adeyemi, but there is more than a hint of fortune about the goal.
Brandt picks the ball up in a pocket of space just inside Celtic's half before playing Adeyemi through on goal, and the German international's strike takes a wicked deflection which wrong-foots Schmeichel.
Karim Adeyemi goal vs. Celtic (29th min, Borussia Dortmund 3-1 Celtic)
It is that man again, but there is certainly no luck about this goal!
Adeyemi picks the ball up just inside the box, and on the most acute of angles he unleashes a ferocious shot into the near post, and while some might question the goalkeeper's role here, you cannot take anything away from the strike.
40th min: Borussia Dortmund 4-1 Celtic (Serhou Guirassy)
It goes from bad to worse for Celtic as Guirassy gets in on the act with a penalty of his own to make it 4-1 to the hosts.
Engels - who set up Celtic's equaliser - clips Adeyemi inside the box and Guirassy goes the same side as Can as he fizzes his penalty past the despairing dive of Schmeichel.
Karim Adeyemi goal vs. Celtic (42nd min, Borussia Dortmund 5-1 Celtic)
Celtic are once again the architects of their own downfall, with Adeyemi once again profiting to pick up his hat-trick.
Maeda is caught in possession on the edge of his own box by Adeyemi, and the German takes just one touch out of his feet before unleashing a pinpoint drive into the bottom corner.
Serhou Guirassy goal vs. Celtic (66th min, Borussia Dortmund 6-1 Celtic)
Dortmund are showing no signs of letting up as Guirassy grabs his second goal of the game to make it 6-1 to the hosts.
The Guinea international picks the ball up just inside the box, and he turns Scales inside out with a delightful piece of skill before calmly slotting the ball home at the near post.
Felix Nmecha goal vs. Celtic (79th min, Borussia Dortmund 7-1 Celtic)
It just gets better and better for Dortmund, who have now scored their seventh goal of the game, this time through Nmecha.
Celtic fail to clear their lines, and the German midfielder picks up the loose ball before unleashing an accurate and powerful strike beyond a helpless Schmeichel.
MAN OF THE MATCH - KARIM ADEYEMI
The German International was in fine form against Celtic by scoring a hat-trick and winning a penalty as Dortmund raced into a four-goal lead at half time.
Adeyemi was a constant threat to Celtic's high line; cutting in and causing chaos with the timing of his runs, and his second goal of the game was an absolute rocket which perfectly encapsulated his scintillating evening - but there will be worries over his fitness after he left the field with an apparent hamstring injury.
BORUSSIA DORTMUND VS. CELTIC MATCH STATS
Possession: Borussia Dortmund 52%-48% Celtic
Shots: Borussia Dortmund 16-9 Celtic
Shots on target: Borussia Dortmund 13-2 Celtic
Corners: Borussia Dortmund 8-4 Celtic
Fouls: Borussia Dortmund 15-6 Celtic
BEST STATS
WHAT NEXT?
An away trip to face Union Berlin in the Bundesliga awaits Borussia Dortmund on Saturday afternoon, meanwhile Celtic are back in Scottish Premiership action on Sunday, when they make the long trip north to face Ross County at Victoria Park.