Fernando Llorente and Georges-Kevin Nkoudou both netted their first goals for Spurs - either side of a fine strike from Son Heung-min - to ensure that the North London outfit come through the group stages with five wins and a draw from six matches.
While Spurs progress as group winners, APOEL finish bottom and miss out on a place in the Europa League to Borussia Dortmund, despite the German outfit losing to Real Madrid.
Spurs wasted little time in applying pressure and after Serge Aurier and Son both sent efforts fizzing wide of the post from close range, the home side somehow failed to take the lead from a free kick.
After Llorente's header was saved, Nkoudou saw a shot from six yards cleared off the line before Davinson Sanchez glanced a header wide from a similar distance.
However, the opening goal did arrive in the 20th minute as Llorente finally got on the board for Spurs, with the Spaniard turning his marker on the edge of the six-yard box before firing into the bottom corner.
Spurs eased off during the middle part of the half but with eight minutes of the opening period remaining, Son doubled their advantage when curling a shot into the corner from 20 yards after being teed up by Llorente.
The home side would have expected more goals after the restart, but it was APOEL who had the better of the early stages of the second half and they could have halved the deficit.
However, Spurs soon restored a level of control over the game without showing the same kind of quality as in the first half, with Nkoudou seeing a shot deflected off target and Son curling a free kick wide of the post from just under 25 yards.
Nkoudou also failed to find the back of the net with a well-struck effort from 14 yards out, but it appeared that both teams were going to go through the motions until the final whistle.
A third goal did arrive, however, through Nkoudou, who scored his first goal in a Spurs shirt with a deflected effort from close range which deceived Nauzet Perez at the near post.
Kazaiah Sterling was given his Spurs debut with two minutes plus added-on time remaining but the remainder of the match was played at a sedate pace as Pochettino's side recorded their first win from four matches in all competitions.
TOTTENHAM HOTSPUR (4-4-1-1): Vorm; Aurier, Sanchez, Foyth, Rose (Walker-Peters 70'); Winks, Sissoko, Alli (Sterling 88'), Nkoudou; Son (Dembele 65'); Llorente
APOEL XI (4-5-1): Perez; Carlao, Rueda, Lago, Vouros; Morais, Vinicius (Sallai 46'), Zahid, Ebecilio, Aloneftis (De Camargo 75'); Pote (Antoniou 81')