Rangers threatened to shock Benfica away from home before failing to qualify for the Champions League group stage for the first time.
Emma Watson’s close-range finish in extra time tied the match at 3-3 on aggregate.
However, a solo goal by Cloe Lacasse of Canada and a late breakaway finish from Jessica Silva gave the Portuguese a well-deserved victory.
Even the late dismissal of defender Lucia Alves could not stop the hosts.
Goalkeeper Victoria Esson, whose own-goal in the first leg gave Benfica the advantage, denied the Portuguese champions a more emphatic victory as they advanced to the group stage for the second consecutive season with a 10th straight win.
Despite making significant alterations to their weekend lineups, both teams had reverted to more familiar lines after collecting impressive domestic victory.
However, the inclusion of Brazilian forwards Nycole Raysa and Valeria in lieu of defender Daniela Ferreira Silva and attacker Marta Cintra appeared to be an attack-minded move by host head coach Filipa Patao.
Throughout the first half, there was no need for defensive cover as Benfica toyed with the first-time Scottish champions.
Ana Vitoria, who had been put back into the home midfield despite scoring twice in the first leg, forced a near post save off Esson’s knees, signalling the start of a surge of raids that pinned the visitors back in their own half.
Esson, making amends for the first-leg gaffe, was twice at full stretch to deny midfielder Andreia Faria from long range and then bravely saved at Raysa’s feet.
Lacasse blasted against the crossbar after defender Ana Seica fluffed her lines in front of an open goal.
After the break, the one-way flow continued, but Benfica’s shots on goal became less accurate, and Rangers began to claw their way back into the game.
Malky Thomson’s side didn’t threaten until the 76th minute, when replacement Watson blasted straight at goalkeeper Rute Costa, while teammate midfielder Chelsea Cornet went wide moments after.
When Costa failed to hold a corner under pressure, Watson poked the loose ball home to tie the game.
Rangers came close to a shock win in normal time thanks to a Nicola Docherty strike that grazed the crossbar, but the full-back was given a clean pair of heels three minutes into extra time when Lacasse walked into the penalty box and fired past the exposed Esson.
Rangers had a late numerical advantage thanks to Alves’ second yellow card, but Benfica still came out on top as substitute striker Silva raced clear to destroy the visitors’ Champions League dream.
