The Polish Ekstraklasa leaders went into the game looking set to become the first side in the tournament's history to record both no points and no goals from their six group stage games.
But the visitors rose to the occasion and eased to victory in a game long since rendered irrelevant by the respective qualifications of group rivals Trabzonspor and Lazio for the next stage.
Legia made a lively start with Jodlowiec coming close after just four minutes and Dominik Furman also missing a chance before Jodlowiec opened the scoring on eight when he headed home from a Brzyski corner.
Apollon goalkeeper Bruno Vale was a busy man in the early stages as he was also forced to save from Vladimirs Dvalishvili and again from Henrik Ojamaa just before the break as Legia were dominant.
With Apollon barely threatening, the Poles extended their lead midway through the second half when Brzyski curled a beautiful free-kick past Vale from outside the box after Ovidiu Dananae was penalised for a foul on Jodlowiec.
Despite the nature of the game both sides were destined to end it with 10 men after Apollon's Gaston Sangoy and Bartosz Bereszynski were both red-carded in the 69th minute.
Apollon belatedly looked for a way back into the game but by the time Rojas Mena had been flagged offside deep in injury time the hosts had missed their chance and Legia claimed a long overdue success.