Llorente had gone 16 games without hitting the net since his summer switch from Swansea but the 32-year-old scored one before setting up a second for Son Heung-min. Nkoudou completed the 3-0 rout late on.
Mauricio Pochettino’s men had secured first place in Group H regardless of this result and they now go through with a spring in their step, after collecting 16 points from a possible 18 in a pool that included Borussia Dortmund and Real Madrid.
Defeat for Apoel means they finish bottom of the standings, while Dortmund take third and a spot in the Europa League.
First place will certainly not guarantee Spurs a kinder tie when the draw is made on Monday.
More immediately, this felt like an important boost to morale for Tottenham, whose mid-season slump has featured just one win in their last five Premier League matches.
It meant starts for Nkoudou, only his third since joining from Marseille 15 months ago, and Llorente, as well as 19-year-old Juan Foyth in defence.
Nkoudou was busy throughout and deserved his goal but Llorente was the most satisfying positive considering he finally showed the sort of sharpness to suggest he can be a valuable alternative to Kane.
Dele Alli, one of the few established players picked, was bright if unspectacular.
Spurs have also suffered from sluggish starts in recent weeks but they were at it from the off here as Serge Aurier and Son both saw early shots flash wide.
Llorente did well to nod a Harry Winks free-kick to the back post but Davinson Sanchez and Nkoudou were both thwarted from close range, the latter’s finish expertly cleared off the line by Jesus Rueda.
Apoel’s resistance could only last so long, however, and Tottenham took the lead in the 20th minute when Llorente was given ample space in the six-yard box to control, turn and slot home Aurier’s driven cross.
Spurs continued to push and probe, with Nkoudou particularly inventive down the left, even if some of his meandering runs appeared to have no obvious destination.
Llorente was more precise and seven minutes before half-time he turned provider, pivoting a neat one-two on the edge of the box with Son, who bent the ball first-time into the bottom corner. It was his fifth goal in his last eight starts.
Apoel striker Mickael Pote could have given his side a lifeline but failed to connect with a free header and after a brief spell of pressure at the start of the second half, Tottenham again took control.
Llorente should have had a second when Rueda scuffed his clearance but the swivelling Spaniard miscued and Danny Rose was perhaps fortunate only to receive a yellow card when he bumped irritably into substitute Roland Sallai.
All that was left was for Nkoudou to cap his dynamic display with a goal. The winger nipped inside Nuno Morais before watching his deflected shot fly into the net.