There were few chances in the first half. The onus was on the home side, but Limassol held firm to go in level at the break.
It looked like an upset could be on the cards as the away team continued to frustrate the Belgian side in the second period.
With 10 minutes to go Anderlecht finally found the breakthrough thanks to a good finish from Dieumerci Mbokani.
The home team finished the tie off when Oleksandr Yakovenko added a second in stoppage time to secure Anderlecht's place in the next phase of the competition.