A win, a draw or even a 1-0 defeat in the Group J clash would have been enough to see the Turkish side into the next stage, but they managed to get the job done in the right way thanks to Adin's treble and a Soner Aydogdu strike.
Trabzonspor will now look to make sure of top spot by avoiding defeat at Lazio - who they lead by two points - in their final group game on December 12.
Apollon made Trabzonspor work hard for the points with goals by Abraham Gneki Guie and Gaston Sangoy making the score 3-2 late in the second half, but it was not enough to avert a loss that brings an end to the Cypriot club's hopes of reaching the next round.
Trabzonspor came into the match as heavy favourites and looking to preserve a 12-game unbeaten run in European competition.
And they wasted little time living up to their billing, the opening goal arriving midway through the first half as Adin nodded in Florent Malouda's cross.
Two minutes later it was 2-0, Aydogdu turning the ball home from close range after more good work from the lively Malouda.
The hosts extended their lead still further just after the hour when Kadir Keles played in Adin and the midfielder fired an accomplished finish high into the net.
Apollon briefly threatened a fightback when Abraham nodded home Giorgos Vasiliou's cross in the 68th minute, and it was 3-2 in the 80th minute when Abraham was hauled down by Keles and Sangoy tucked away the resulting penalty.
An equalising goal for the visitors would have been a headache for Trabzonspor ahead of their decisive game in Rome in a fortnight, but any jitters were erased in the 83rd minute when Adin guided a free-kick into the bottom right corner to wrap up his treble and the points.