Spurs' place had been all but secured by a 6-1 victory at White Hart Lane in the first leg, meaning Martin Jol could hand a debut to summer signing Kevin-Prince Boateng.
Seven minutes in Jermain Defoe wasted a clear chance to open the scoring as he fired over the crossbar from 12 yards, following Darren Bent's set-up work.
As time ticked on there was little by the way of goalmouth action, with Spurs content to sit on their lead and not exert themselves too much. On the half-hour mark a couple of set-pieces caused alarm in the visitors' area, but eventually the danger was cleared.
Ten minutes before the break an unmarked Defoe should have broken the deadlock, but fired his shot straight at the keeper after taking the ball down 12 yards from goal.
Steed Malbranque set up Defoe again just before half-time, but the England man hit the post when it seemed easier to score.
Nine minutes into the second half Anorthosis went in front as Nikos Frousos brought down a cross from the left and from his lay-off, Fabinho smacked home a left-foot drive with the aid of a slight deflection.
Defoe's jinking run just past the hour mark almost opened up the home defence, before the same player fired wide from just outside the area soon after.
Sixteen minutes from time Vincent Laban threatened to double the home side's lead as his fizzing left-footer flew inches wide of the post with Paul Robinson rooted to the spot.
However, sub Robbie Keane drilled home an equaliser four minutes later, converting a ball in from the left by fellow replacement Gareth Bale to make the score 1-1 on the night.
That proved to be the end of the scoring as Spurs played out time with some ease.