Jorge Jesus' home side began to dominate from the start and it did not take them long to turn that into goals as Djuricic broke the deadlock in the fourth minute at Estadio da Luz.
The Serbia striker collected the ball in the centre of the Anderlecht goal and drilled it home with a close-range strike to give Benfica the lead.
The visitors took a while to get into the game and it was 17 minutes before they had their first real chance on goal.
But Benfica goalkeeper Artur was quick to react as he caught Aleksandar Mitrovic's close-range header to deny an equaliser.
Oscar Cardozo then had a couple of chances in quick succession to double the home side's lead, but both times Anderlecht stopper Silvio Proto was on hand to keep his efforts out.
And it was not long before the Portuguese side doubled their advantage as Andre Almeida's header from the right found Luisao, who slotted home from the centre of the box to make it 2-0.
Benfica carried on going forward and Cardozo came close to adding his name to the scoresheet minutes before half-time, but his long-range effort sailed over the crossbar.
Anderlecht coach John van den Brom brought on striker Frank Acheampong for midfielder Demy De Zeeuw in a tactical move to provide more firepower at the start of the second half.
Both sides were slow at coming forward as the half got under way and Van der Brom's tactics almost paid off as Luka Milivojevic came close to scoring a leveller, but his 20-yard effort cleared the crossbar.
Anderlecht began to enjoy the best of the second-half exchanges as Mitrovic came close to netting after receiving Fabrice N'Sakal's cross, but his header was tipped round a post by Artur.
Luka Milivojevic was the next to be denied by Artur as the away side pressed for a goal to reduce the deficit, but they could not find one.