Fernando Llorente was signed in the summer to provide back-up for Harry Kane and finally opened his account for Tottenham in his 17th appearance for the club.
It was a night for B-listers with manager Mauricio Pochettino making wholesale changes – and so did Alli, whose commercial interests will henceforth be taken care of by Creative Artists Agency.
With Spurs guaranteed to finish top of Group H, the Argentinian simply did not need his headline acts.
Alli was just one of three players in the starting line-up who were also named in the team who drew at Watford on Saturday, with Son Heung-min
and Davinson Sanchez also pushed into action .
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Of course, the England star was not the only one looking to build a bit of confidence. Llorente had spurned a move to Chelsea to join the Tottenham cause and, three months in, certainly had something to prove.
However, after just nine minutes he spurned his best chance to find the back of the net for the first time since scoring for Swansea on the final day of last season, when he failed to bury a sublime Son free-kick cross past keeper Nauzet Perez.
Indeed, the visitors’ goal seemed to be leading a charmed existence.
Georges-Kevin Nkoudou’s follow-up hit the only player on the line, Jesus Rueda, and when the ball was played back in, Sanchez contrived to glance it wide from just three yards out.
But Llorente’s moment duly arrived in the 20th minute.
Serge Aurier’s cross was behind him, but the Spain international refused to panic, using all the time available to him to trap, turn and shoot Tottenham into the lead.
Then it was two. Moussa Sissoko, Son and Llorente combined quickly to provide the opening for Son to curl a left-footed shot inside the far post for the second in the 37th minute . Alli, whose last appearance here in this competition was marked by that rare double against Real Madrid, remained a frustratingly peripheral figure as the game passed him by.
Llorente and Son, meanwhile, combined well for the latter to test Perez yet again before the break and with Tottenham completely dominant, there was polite applause at the interval.
The thunderous way that the long-coated figure of Pochettino marched into his inner sanctum for the half-time talk suggested a less polite reception awaited the Tottenham players.
If anything, though, it was APOEL who re-emerged the more energised, and Danny Rose only just managed to deflect a Praxitelis Vouros effort past the far post shortly after the restart.
It took Spurs 12 minutes to mount a serious attack, Llorente badly miskicking from Rose’s cross but Aurier tested the goalkeeper from the loose ball. Son hit a 30-yard free-kick a couple of feet over the bar.
Finally, Nkoudou twisted and turned his way more menacingly into the area and a deflected shot made it three with 10 minutes to go.
It was a cue for Alli’s withdrawal – killed off before the final reel when he was replaced by impressive 19-year-old starlet Kazaiah Sterling.
His single moment in the centre of the action had been when he got involved in an unseemly tangle with the APOEL goalkeeper as he looked to clear the ball – yet another flash of that infamous devilment. Luckily, Slovenian referee Salvko Vincic looked upon the incident benignly.
Even with fancy new representatives, on the basis of this performance, nobody was still prepared to give him a booking.
TOTTENHAM (4-2-3-1): Vorm, Aurier, Sanchez, Foyth, Rose (Walker-Peters 70), Winks, Sissoko, Alli (Sterling 88), Nkoudou, Son (Dembele 65), Llorente. Booked: Aurier, Rose. Goals: Llorente 20, Son 37, Nkoudou 80.
APOEL (4-2-3-1): Perez; Vouros, Rueda, Carlao, Lago; Vinicius (Sallai 46), Morais; Zahid, Ebecilio, Aloneftis (De Camargo 75); Pote (Antoniou 81). Booked: Sallai, Rueda.
Referee: S Vincic (Slovenia).