Winless so far in the league phase, Copenhagen had two significant warnings in the opening 20 minutes, as Pantelis Hatzidiakos deflected a Xavi Simons shot wide, before Pedro Porro sent a dangerous-looking free kick narrowly over the bar.
But it was third time lucky for Tottenham soon after, when a dreadful giveaway from Gabriel Pereira’s failed pass in Spurs territory allowed Simons to steal possession.
He spotted Brennan Johnson’s perfectly-timed run and threaded the ball through to the Welsh international, who - despite being at a narrow angle just right of goal - was able to roll the ball nonchalantly into the far corner past the overcommitted Dominik Kotarski, for his first strike in eight matches.
Spurs perhaps should have capitalised on this more than they did, but instead allowed Copenhagen to regroup somewhat - ill-advised against a side that boasted 18 different goal scorers across the season ahead of kickoff.
But after Elias Achouri fired comfortably over the Spurs bar on a rare Copenhagen attack, Tottenham nearly scored a sensational second five minutes before half-time.
Some incredible interplay between Wilson Odobert and Simons around the Copenhagen box saw them exchange four one-touch passes - including a defence-splitting flick into the box from the latter - but when Randal Kolo Muani got Simons' final ball misaligned with his feet, he could only fire wide at close range.
Thomas Frank’s men doubled their advantage five minutes after the interval, when a long ball down the right flank saw Muani charge through and force Kotarski into coming out again.
While the goalkeeper blocked Muani’s initial attempt to dink past him, the ball deflected wide for him to pull back to Odobert, who fired into the gaping net.
After Youssoufa Moukoko almost made it 2-1 as he curled an effort that was held well by Vicario, Spurs were reduced to 10 men when Johnson’s cynical challenge on Marcos Lopez’s ankle saw his initial yellow upgraded to a red.
There might have been some expectation of a real game, but instead, Spurs went into overdrive and scored twice in just a matter of minutes, with their third of the night being a goal of the season contender from Micky van de Ven, who stole the ball near his own box and charged downfield past no less than five opponents before firing assertively into the net.
Copenhagen barely had time to take stock before it was 4-0, with Cristian Romero bursting through the middle and squaring for Joao Palhinha to power in.
Understandably, the tempo somewhat lulled, though there was still time for Richarlison to head against the bar, and then hit it from the penalty spot after Dane Scarlett was hauled down inside the box in injury time.
While it wasn’t the double-figures rout it could have been, Tottenham’s first four-goal haul under Frank is undoubtedly something to build on, even if the opposition was vastly inferior from the first whistle.
Copenhagen themselves looked like little more than cannon fodder, and could find themselves as low as second-bottom of the league phase table in 24 hours’ time, after failing to net for a 13th occasion in 14 away losses across all UEFA competitions.
Flashscore Man of the Match: Xavi Simons (Tottenham Hotspur)
