Both teams lost their opening group games but Basel took just two minutes to put their 3-0 defeat by Manchester United behind them when Michael Lang struck from inside the area after a break on the left.
Basel effectively killed off the game with a stunning second on 21 minutes when Renato Steffen mounted a counter-attack from deep inside his own half and found Oberlin who threaded a neat finish through keeper Julio Cesar's legs.
A bad night for Benfica's 5,000 travelling supporters turned rapidly worse with Dutchman Ricky van Wolfswinkel scoring Basel's third from the penalty spot after Lubomir Fejsa felled the ever-dangerous Oberlin.
The 68th-minute dismissal of Andre Almeida for a wild two-footed lunge on Luca Zuffi made the home side's task that much easier with Oberlin adding his second and Blas Riveros their fifth as Benfica suffered their first competitive loss to a Swiss side.
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(Reporting by Neil Robinson, editing by Ed Osmond)
