Van de Ven and Djed Spence were forced to apologize to Tottenham boss Frank this week after they ignored his plea to applaud fans following Saturday's loss to Chelsea.
The pair, frustrated by boos from angry Tottenham fans during the Premier League defeat, walked straight down the tunnel rather than follow Frank's order.
But Van de Ven retained his place in the starting line-up and made peace with his manager and the supporters with a Champions League moment of magic.
He ran over half the length of the pitch before delivering a clinical finish that ranks among the best goals scored in the Champions League so far this season.
By then Tottenham were already leading by two goals thanks to strikes from Brennan Johnson and Wilson Odobert in north London.
Johnson was sent off in the second half when his lunge on Marcos Lopez was upgraded from a booking to a red card after VAR intervened.
Joao Palhinha netted the fourth goal as Tottenham won for only the second time in their last six matches in all competitions.
Saluting Van de Ven's wonder-goal, Frank invoked Argentine superstar Messi.
"That could be the goal of the season. It was like Messi turned into a centre back," he said.
Van de Ven added: "I started dribbling and I thought I would see if they would catch up. They didn't. I felt amazing."
Frank's side remain unbeaten in this season's Champions League with two wins and two draws ahead of their trip to holders Paris Saint-Germain later in November.
Tottenham had produced only one shot on target against Chelsea as they endured yet another dismal defeat on home turf in 2025.
But this was exactly the kind of attacking display that Tottenham fans demand, albeit their first home win since September 24 came against weak opponents.
"In life and football after a bad performance or situation it is about how you react," Frank said.
"Our players have had a great bounce-back mentality in the last few days. They have wanted to turn things around and win. We controlled it from minute one and even after the red card."
Slick Spurs
Frank's men were gifted the lead in the 19th minute.
Xavi Simons' incisive long pass sent Johnson racing through on goal, prompting goalkeeper Dominik Kotarski to rashly race out of his area.
Kotarski made a complete hash of the attempt to intercept Johnson's run and the Wales winger calmly slotted into the empty net from an acute angle for his first goal in nine matches.
Tottenham made it two in the 51st minute and once again Kotarski was at fault as he recklessly sprinted out of his area and smashed a panicked clearance straight at Randal Kolo Muani.
The ball looped over Kotarski and Kolo Muani rolled it back to Odobert, who slotted home from close range.
Johnson was dismissed in the 55th minute after clattering into Lopez, a needless challenge that initially earned a yellow card from Erik Lambrechts before VAR sent him trudging to the dressing room.
Tottenham were still far too slick for Copenhagen and Van de Ven sealed the game in the 64th minute.
Advancing from inside his own half, the Dutch centre-back swept through the Copenhagen defence, evading a pair of tackles before smashing a fine low finish beyond Kotarski from just inside the area.
Van de Ven cheekily cupped his ear to the crowd before team-mates made a point of embracing him to show their support after Saturday's spat.
Palhinha slid a clinical finish past Kotarski from six yards in the 67th minute.
Richarlison should have made it five but he blasted a stoppage-time penalty against the bar after Dane Scarlett was fouled by Viktor Claesson.