كتب : Amro Hassan
An Adriano header in the 44th minute was the only difference between the two sides as Inter maintain Champions League B with seven points.
Jose Mourinho's side could have taken the lead in the 3rd minute, but Brazilian full back Maicon placed free header wide.
The visitors nearly caused an upset through a Traianos Dellas free kick, but Francesco Toldo was up for the task with a diving save to keep the game goalless.
On ten minutes Sulley Ali Muntari had a good effort saved by Famagusta keeper Arjan Begaj's before Adriano saw another shot whistle off the post.
One minute before the interval Inter scored after a nice Zlatan Ibrahimovic pass found Maicon, the Brazilian cut inside and his beautiful cross set up Adriano's free header.
In the second half, and with no threat from Famagusta's side, Inter were more than happy just to kick the ball around until the final whistle was blown.
In the group's other game, Panathinaikos drew 2-2 with Werder Bremen in Athens.
Per Mertesacker took the lead for the Germans before a Vangelis Mantzios brace (36, 68) nearly won the game for the home side.
Bremen salvaged a point seven minutes from time courtesy of a Hugo Almeida header.
The draw earns Panathanaikos their first point of the competition as they lie bottom of the group with Bremen in third with four points.