Spurs were always facing a tall order in Thursday’s round-of-16 second-leg tie at the Estadio da Luz in Lisbon, after losing 3-1 in last week’s encounter at White Hart Lane.
Ezequiel Garay scored the opening goal in the 34th minute when he rose above Sandro to head home Eduardo Salvio’s right-wing cross.
That extended Benfica’s aggregate advantage to three goals, but they were stunned in the 78th minute when Chadli drove home a fierce equaliser from outside the box.
The same player then swivelled and shot home from close range a minute later to put the visitors in front, and Spurs had a penalty appeal turned down in the 88th minute as substitute Harry Kane looked to be bundled over in the box.
But instead, Benfica won a spot-kick at the other end in stoppage time when Sandro barged into Lima, and the same player stepped up to equalise on the night with the last kick of the game.
That ensured the Portuguese side’s long unbeaten run was stretched to 26 games and that they would be in Friday’s draw for the last eight.
Around 3,000 travelling supporters made the trip to Lisbon, where Tim Sherwood made five changes to the Spurs team that lost 1-0 at home to Arsenal in the Premier League on Sunday.
Brad Friedel replaced Hugo Lloris in goal, while Zeki Fryers came in at centre-back. With Jan Vertonghen suspended and Younes Kaboul injured, Sandro filled in in central defence, as Gylfi Sigurdsson was recalled into the midfield along with Aaron Lennon, who captained the team. Christian Eriksen dropped to the bench, which also consisted of Harry Kane and a host of reserve-team youngsters. Emmanuel Adebayor was also among the injury absentees, so Roberto Soldado led the line.
Luisao, who scored twice from set pieces in the first leg, directed a ninth-minute corner wide.
Spurs had a chance of their own soon after when a corner was flicked on to the unmarked Soldado, who controlled well only to hit a strike into the ground and wide.
A last-ditch block then meant the Spaniard was unable to convert Chadli’s cut-back. The resulting corner saw Chadli head tamely wide.
Benfica, though, went ahead on the night in the 34th minute as Salvio saw off Lennon and clipped in a fine ball for Garay to powerfully header home.
Early in the second half, Sigurdsson almost latched onto a neat Andros Townsend ball from the left.
The England winger was enjoying his duel with Maxi Pereira – someone he may again come up against at the World Cup in the match with Uruguay – and soon impressively cut past him again, only for his fierce strike to hit the side-netting after a slight deflection.
A wonderful Sandro tackle on Ruben Amorim thwarted the Benfica midfielder, before Guilherme Siqueira missed the goal marshalled by Friedel.
Kane was brought on in a bid to grab a leveller and started a move that resulted in Chadli firing at Benfica goalkeeper Jan Oblak, who the Belgium international did beat with 12 minutes remaining as he cut in from the left and lashed home a 20-yard drive.
Spurs then netted a quickfire second. Kane knocked a back-post Eriksen cross into the path of Chadli, who impressively turned to fire a left-footed half-volley into the far corner.
The visitors sensed a shock, and Luisao did well to deny Lennon the opportunity to roll into an empty net.
Spurs continued to press after Salvio forced Friedel into a save, with Kane having penalty claims rejected by Slovenian referee Damir Skomina after being upended in the box by Miralem Sulejmani.
Oblak made fine saves to deny Sigurdsson and Kane as the visitors continued to press, only to get caught by a stoppage-time sucker-punch as Lima netted after being brought to the deck by Sandro.