Tim Sherwood's side will have to score at least three goals themselves in the Estadio da Luz in Lisbon next Thursday night to have any chance of progressing through to the quarter-finals.
Rodrigo netted the only goal of the first half with an excellent finish from Ruben Amorim's pass down the right channel and Luisao headed in an Amorim corner on 58 minutes to extend their lead.
Although Christian Eriksen's superb 20-yard free-kick reduced the arrears six minutes later, Luisao lashed home a fierce close-range effort in the 84th minute to give Jorge Jesus' men a comfortable advantage.
The Benfica coach, whose team is now unbeaten in 24 games in all competitions, angered Sherwood with his touchline antics at White Hart Lane but there could be no arguments over who deserved to win on the night.
Sherwood made three changes to the Spurs line-up that began the 4-0 Premier League defeat to Chelsea at Stamford Bridge last time out. Harry Kane made only his second start of the season, while Eriksen returned after two games out with a back injury. There was also a recall for Paulinho. Nabil Bentaleb dropped to the bench, while Michael Dawson (hamstring) and Gylfi Sigurdsson missed out. Danny Rose had been struggling with a knee injury but he was named among the substitutes.
After Sandro's early booking, the same player blasted a shot over the crossbar before Spurs won a flurry of corners. The home team's best first-half chance came when Slovenia goalkeeper Jan Oblak let captain Younes Kaboul's headed clearance go past him, but he recovered in time to dive on the ball before Eriksen could reach it.
Just before the half-hour mark, Kyle Naughton was caught out in the left-back position, as a pass from Amorim down the right channel was threaded through perfectly for Rodrigo. The former Bolton loan signing took the ball on and finished superbly, stroking a low left-footed shot with slight curl across Hugo Lloris and inside the far post.
Spurs were jeered off at half-time, but they carved out a great opportunity soon after the restart. Luisao played Emmanuel Adebayor onside from Eriksen's pass, only for the big striker to scuff his shot poorly - and the ball skewed wide of goal.
Aaron Lennon shot straight at Oblak, while Lloris had to be alert to tip over Amorim's shot at the other end after Kane had been easily dispossessed.
But from the resulting 58th-minute corner, Amorim swung the ball into the box where Kaboul was not marking Luisao closely enough. The Brazilian centre-back nodded the ball past Lloris for his side's second goal of the night.
Spurs responded after Kane won a free-kick just outside the Benfica box on 63 minutes, right-back Silvio bringing him down. Eriksen stepped up to take the set-piece from 20 yards out, and curled the ball over the wall and into the top corner, to the right of Oblak.
Lloris was almost punished by Rodrigo when he let the ball bounce over his head, with Sherwood then introducing Roberto Soldado in place of Kane.
However, on 84 minutes, Benfica restored their two-goal advantage. Lloris saved Ezequiel Garay's initial downward header after a free-kick wide on the left, but Luisao was first to pounce in the area and smash home his second goal of the evening off the underside of the bar from a tight angle.
The goal led Jesus to show three fingers to Sherwood, antagonising the Spurs boss at the end of a match in which the managers did not shake hands.
Spurs must recover quickly as they host Arsenal in the north London derby on Sunday afternoon, before travelling to the Portuguese capital for the second leg against Benfica in seven days' time.