The Premier League side was outclassed by the impressive Portuguese outfit on Thursday, with two goals from the defender all but deciding the tie
Arsenal and Manchester City had already crashed out of the Champions League on Tuesday and Wednesday respectively. Spurs will need to come from behind for the second time in as many rounds if they are to make the quarterfinals 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 goals in as many matches.
With progression looking an unlikely prospect for Spurs after the second strike, Christian Eriksen pulled a goal back with a 64th-minute free kick, but Luisao dashed Tottenham hopes in the closing stages when he found the net in the aftermath of a Benfica set piece.
The result represents Spurs' first home defeat in 12 European fixtures, and Benfica's three away goals leave Tim Sherwood's team with a mountain to climb in next week's second leg.
Sherwood handed Harry Kane just his second start of the season after openly criticizing his side that crumbled to a 4-0 Premier League defeat at Chelsea on Saturday.
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 defense-splitting Ruben Amorim pass before finding the bottom left-hand corner of the goal with a low 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.
Tottenham goalkeeper Hugo Lloris had to be on high alert in the 57th minute as he tipped over an Amorim effort after Kane had sloppily conceded possession, but it was not long before the visitors doubled their advantage.
From the resulting corner, Luisao shook off his marker to head beyond a helpless Lloris.
The two-goal advantage did not last long as Eriksen curled home a superb free kick shortly afterwards to salvage some hope for the London club.
Benfica may have ended Tottenham's chances in the competition in the 84th minute though, as Luisao smashed home from close range after Lloris could only weakly parry Ezequiel Garay's header into the defender's path.
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 quarterfinals with a fine away win.