Not since November 2014 had the Swiss side tasted victory at this level, but their Group A opponents were blown away by a devastating game plan that relied heavily on the awesome speed of Oberlin to secure the club's biggest Champions League win.
The Red Bull Salzburg loanee ran riot, playing a key role in Michael Lang's breakthrough goal before adding a brace of his own either side of the penalty he won for Ricky van Wolfswinkel to convert.
Rui Vitoria, hurting from a home reverse against CSKA Moscow on matchday one, had called for his side to deliver in the first of "five finals", but the coach's tactics left Benfica wide open, while his attempts to outsmart Basel - dropping Switzerland international Haris Seferovic - blunted the attack.
Although the hosts, two up after 20 minutes, thrived on defending their lead, further goals were always likely with Oberlin on the pitch and Andre Almeida's dismissal for an outrageous challenge on Raoul Petretta - shortly after the third - ended the game as a contest.
Blas Riveros - Petretta's replacement - netted a fifth to complete Benfica's humiliation.
Basel's pace and energy was evident from the off and they were rewarded with the opener inside two minutes.
Oberlin drove at the visitors' defence and slipped a pass through for Renato Steffen, tempting the ambling Julio Cesar from his goal line to hand Lang a simple, uncontested finish when the ball eventually broke his way on the right-hand side of the area.
Benfica sought a response, but their pressure only played into the hands of the counter-attacking hosts. Oberlin again did the damage, timing his run beautifully to sprint clear and calmly convert through the goalkeeper's legs.
Oberlin continued to run at Benfica - with 36-year-old Luisao, in particular, struggling - but both Taulant Xhaka and Lang wasted promising shooting opportunities.
Although Raul Jimenez awkwardly prodded over in a rare opening for the visitors at the end of the first half, Basel were swiftly back on the attack after the restart and Raoul Petretta's strike drew a save from Julio Cesar.
Lang passed up a great chance to put the result beyond doubt as he fired wide, but it mattered little; another incisive Oberlin run teased a foul from Lubomir Fejsa inside the area.
Van Wolfswinkel dispatched the spot-kick and Benfica's task quickly became harder still, with Andre Almeida foolishly crashing into Petretta's shins and then having the cheek to challenge his inevitable red card as the understandably outraged home supporters angrily gestured in his direction.
Luisao had suffered throughout and Oberlin made a mockery of his ageing legs on the fourth goal, dancing past a mistimed challenge on the edge of the box to nutmeg Julio Cesar once again.
Steffen tested the goalkeeper shortly afterwards, before Raphael Wicky took mercy on Luisao and his floundering team-mates with the withdrawal of Oberlin.
Basel's momentum was scarcely interrupted, though, and substitute Riveros poked in the fifth, having struck the post moments earlier after a Mohamed Elyounoussi effort had also struck the woodwork.