The Spaniard joined Mauricio Pochettino’s side at the end of August but has struggled in the shadow of Harry Kane this season and has largely been limited to substitute appearances.
Kane was rested for the visit of the Cypriot champions, though, and Llorente excelled in his absence, scoring a wonderful first midway through the opening period before turning provider for Son Heung-min’s superb goal in the 37th minute.
The hosts eased off in the second half and rarely threatened, but Georges-Kevin N'Koudou added a deserved gloss to the scoreline in the 80th minute with a deflected effort.
Tottenham have struggled in recent weeks – winning just one of their last five games prior to this win – but they never looked in danger of failing to take three points in a game they dominated from start to finish.
The victory sees them finish top of Group H with five wins and a draw from their six games and now face an anxious wait until Monday, when they find out who they will face in the last 16.
Pochettino made eight changes from the weekend draw with Watford and handed a first start of the season to N’Koudou.
His new-look side did not take long to settle into their stride, however, and nearly scored twice in the opening three minutes as Serge Aurier and Son both flashed shots just wide of Nauzet Perez’s goal.
An almighty goalmouth scramble soon followed that somehow failed to result in a Tottenham opener. Llorente’s initial header was eventually bundled into the path of N'Koudou, whose point-blank effort cannoned off Jesus Rueda’s head on the line before Davinson Sanchez conspired to head wide from Llorente's clipped cross.
Llorente then opened his Tottenham account in the 20th minute as he controlled Aurier’s incisive cross, swivelled and then finished past Perez in one almost-balletic movement.
Spurs' first-half dominance was rewarded with a second eight minutes before the interval. Son's pass to Llorente on the edge of the penalty area was cushioned back into his path and the South Korean whipped a fierce effort into Perez's right-hand corner for his second goal in two games.
APOEL, who had offered almost nothing in the way of attacking threat in the opening period, started brightly after the break and almost reduced the deficit when Praxitelis Vouros' drive was deflected just wide by Danny Rose.
Tottenham’s comfortable evening nearly suffered an unnecessary setback midway through the second half when Aurier raked his studs down Efstathios Aloneftis’ ankle. Referee Slavko Vincic deemed the challenge to be worthy of just a yellow card, though, much to the relief of the Ivorian.
It was a largely uninspiring second-half performance by Tottenham, but they did grab a third with 10 minutes remaining as N’Koudou picked up Dele Alli's pass and sent a heavily deflected effort past the helpless Perez for his first goal for the club.
Key Opta stats:
- Cypriot sides have never tasted victory against English opposition in 15 attempts in European competition (D3 L12).
- Fernando Llorente scored his first ever goal for Spurs in what was his 17th appearance for them in all competitions.
- In fact, Llorente scored his first goal in the Champions League since December 2015 whilst playing for Sevilla against Juventus; 729 days ago.
- Fernando Llorente both scored and registered an assist in a single Champions League game for the first time in his career.
- Kazaiah Sterling became the youngest ever player to represent Tottenham Hotspur in the Champions League at 19 years and 27 days.