Two quick goals gave Tim Sherwood's side unexpected hope but Ezequiel Garay's first-half strike and a late penalty saw the hosts through.
The hosts looked on course for a comfortable 1-0 win at the Estadio da Luz thanks to Ezequiel Garay's thunderous first-half header after winning the first leg 3-1 at White Hart Lane.
Yet there was a dramatic ending as Nacer Chadli's quick-fire double sparked a late Spurs comeback. But Lima's last-gasp penalty denied the London club victory on the night as Benfica remained in contention for a second consecutive Europa League final.
Jorge Jesus's Primeira Liga leaders can now look forward to the quarterfinals, while Tottenham's gutsy exit may alleviate some of the pressure on boss Tim Sherwood.
Benfica missed a great opportunity to extend its aggregate lead as early as the ninth minute when Garay nodded the ball into the path of center back partner Luisao but he could only head over the crossbar from 8 yards out when unmarked.
That miss could have been punished by Roberto Soldado six minutes later when the Spanish striker controlled the ball at the back post before his half-volley went down into the turf and wide of the target. It was an open contest and Tottenham spurned another chance to take the lead after 26 minutes, with Chadli heading Gylfi Sigurdsson's corner wide.
Benfica took advantage of the visitors' wasteful finishing in the 34th minute as Eduardo Salvio ghosted past stand-in captain Aaron Lennon on the right before clipping an inviting cross into the box, which Garay finished with a thumping header.
The visitors looked comfortable in possession for the remainder of the opening period and continued that trend in the second half. Luisao could have had his third goal of the tie in the 58th minute when he leapt highest to head Miralem Sulejmani's corner wide.
With tie seemingly petering out to a Benfica win, Tottenham turned the game on its head after 78 minutes as Chadli cut in from the right flank and rifled a right-footed shot into the far corner. Just a minute later, Chadli scored his second when he spun on the spot and hooked his shot in the top-right corner.
There was further drama in the closing stages when Suljmani felled substitute Harry Kane in the area but the referee did not award the penalty.
Benfica was then grateful to goalkeeper Jan Oblak deep into injury time as first he kept out Sigurdsson's header with a fine point-blank save before holding Kane's tame header.
The hosts then settled the game as Lima equalized from the spot, after Sandro had fouled the midfielder in the area.