Arsenal and Manchester City had already crashed out of the UEFA Champions League on Tuesday and Wednesday respectively, and Spurs will need to come from behind for the second time in as many rounds if they are to make the quarter-finals after a disappointing home defeat.
Rodrigo scored the opener on the half-hour mark before Luisao doubled the advantage after the break – both scoring their second goal in as many matches.
The result represents Spurs' first home defeat in 12 European fixtures, and Benfica's three away goals leave them with a mountain to climb in next week's second leg.
The hosts enjoyed plenty of possession in their opponents' half as the first period progressed, but Benfica goalkeeper Jan Oblak remained unchallenged aside from a Kyle Walker free-kick from which Younes Kaboul was deemed to have impeded the Slovenian goalkeeper.
Despite Spurs' greater share of possession, it was the 2013 Europa League runners-up who drew first blood as Rodrigo latched onto a defence-splitting Ruben Amorim pass before finding the bottom left-hand corner of the goal with a low left-footed effort.
Eriksen – who returned from a back injury – threaded the ball into the path of Emmanuel Adebayor shortly after the break, but the striker dragged his attempt well wide of the left-hand post before Aaron Lennon directed a tame strike straight at Oblak.
Benfica looked to have ended Tottenham's chances in the competition in the 84th minute though, as Luisao smashed home from close range after Lloris had kept out Ezequiel Garay's header.
The goal prompted a frank exchange of words between Sherwood and Benfica boss Jorge Jesus but it was the latter who had the last laugh, as his side put one foot in the competition's quarter-finals with a terrific road win.
