The Europa League runners-up went in front when forward Djuricic, 21, pounced on the rebound after keeper Silvio Proto could only parry a fourth-minute shot.
Benfica were in control throughout and Brazilian Luisao extended their lead with a neat volley after 30 minutes.
The Belgian visitors perked up after the break and were unlucky when they had a goal disallowed for offside.
Benfica seemed content to settle for the two-goal victory margin in the second period as they claimed their first clean sheet of the season.
"We were very superior in the first half," said coach Jorge Jesus. "We would like to score lots of goals and massacre our opponents ... but not even Barcelona do that."
Anderlecht struggled in attack and rarely penetrated Benfica's all-Serbian midfield wall of Nemanja Matic and Ljubomir Fejsa.
"It's always good to lend a hand up front and score but I am particularly happy we kept a clean sheet," Luisao said.
The Estadio da Luz will stage this season's Champions League final.
In the other Group C match, Paris St Germain romped to a 4-1 win at Olympiacos.