The Portuguese outfit never looked in serious danger against its Belgian opponents, and made a positive beginning to its group thanks to a pair of early goals
First-half goals from Filip Djuricic and Luisao gave the home side an early advantage that they were not prepared to relinquish and they now find themselves comfortably off the mark in a tough group.
Despite a number of injuries, Jesus named a strong lineup, with 19-year-old Lazar Markovic, who was heavily linked with Chelsea in the close-season, leading their attack.
Meanwhile, Anderlecht coach John van den Brom also opted to showcase youth in his side, with 16-year-old Youri Tielemans named on the bench.
There was a return for goalkeeper Silvio Proto, who was a doubt for the clash with a stomach injury but shook off that problem to be involved.
However, within five minutes he was picking the ball out of the net as Benfica went ahead through Djuricic. The Serbia international responded quickest when Proto parried an earlier effort back into his path, and he had no problem in converting.
Things did not get any easier for the visitors and Oscar Cardozo looked set to tee up a teammate in the 17th minute after easing past two defenders, but his cross was lacking.
And, despite the determined resilience of the Belgian side, Luisao doubled Benfica’s advantage after half an hour. The 32-year-old showed plenty of skill to chest down a header from Andre Almeida and then volley neatly past Proto, leaving the Belgium international with no chance.
Anderlecht did have a chance to get back in the game just before halftime, but Luka Milivojevic wasted his effort following a corner.
Whatever was said by Van den Brom at the interval appeared to work as they came out with a renewed fight and immediately began to press their hosts.
They almost had goalkeeper Artur Moraes beaten soon after the restart, but the Brazilian just got outstretched fingers to a header from 19-year-old Aleksandar Mitrovic after 57 minutes.
However, it was Cardozo who perhaps had the best chance of the half after receiving a ball into the box only to react slowly and prod wide.
Anderlecht had no intention of giving up without a fight and it looked like the club had gained a consolation in stoppage time when Matias Suarez connected with a free kick from Dennis Praet, but his effort was well saved.
Anderlecht will now face Olympiakos on Oct. 2, while Benfica will look for more of the same when it faces Paris Saint-Germain.