Brazilian Bruno Cesar finished off a polished move in the 20th minute and beanpole Paraguay striker Oscar Cardozo, who had been on the field for just five minutes, took advantage of a shoddy defensive wall to fire the second 15 minutes from time.
For the Swiss champions, who drew 3-3 at Manchester United in their previous Group C match having come within a minute of winning, it was a return to the sad routine of home European defeats.
Basel crashed out of the Europa League after losing at home to Fulham two seasons ago and suffered home defeats to Bayern Munich and AS Roma in the Champions League last term as they went out in the group stage.
"The first 45 minutes were very good, we commanded the game," said Benfica coach Jorge Jesus, whose team top the group with seven points.
"We had more possession and were strong in defence," he added after being ordered off the bench by the referee in the closing minutes for dissent.
The Swiss were playing under interim coach Heiko Vogel after Thorsten Fink, who guided them to two successive domestic titles, quit last week to join Hamburg.
"That's not why we lost, Vogel prepared us very well. We are convinced he is the right man for the job," said striker Marco Streller.
Benfica started with eight South Americans - four Brazilians, three Argentines and a Uruguayan - and no Portuguese in their line-up.
Their influence was reflected in their slick passing and flair with Nicolas Gaitan and Pablo Aimar, two Argentines overlooked by their struggling national side, pulling the strings in midfield. Basel were workmanlike in comparison.
Left-footed Gaitan, 23, was especially threatening and set up the first goal as he ran at the Basel defence, exchanged passes with Aimar, then sent an inviting pass across the penalty area.
Quick-thinking Rodrigo dummied to leave his fellow Brazilian Bruno Cesar with a free chance and he side-footed home.
"They're technically strong and it was a very well-made goal," said Streller.
Benfica did not have it all their own way and needed good saves from Brazilian goalkeeper Artur to deny Streller and Xherdan Shaqiri before half-time.
The twice European champions continued to control possession after half-time and Aimar should have done better when he was found unmarked by Luisao's long ball upfield, but he shot weakly at Yann Sommer.
Emerson was also denied by Sommer while Artur made another fine save at the other end to deny Streller from close range.
Cardozo, surprisingly left on the bench, came on in the 70th minute and needed only five minutes to secure the three points. Benfica won a free-kick 25 metres out and Cardozo's effort found a huge gap in the two-man defensive wall and flew into the net.
The last few minutes were uncomfortable for the visitors who had Emerson sent off for a second yellow card and coach Jesus dismissed from the touchline.
"That's a risk I run from the way I live the game," said
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