With the comfort of a 1-0 lead from the first leg, the Portuguese withstood Bordeaux's early attacks before snatching a lead through Jardel's header.
Cheick Diabate gave the hosts a slither of hope with 16 minutes left but it was extinguished seconds later by Oscar Cardoza as Benfica made certain of the win.
The teams exchanged further goals in the dying seconds, with Jardel scoring an own goal before Cardoza replied instantly with Benfica's third.
Bordeaux, who ended a dismal domestic run with a 1-0 win over Bastia at the weekend, began in determined fashion.
Diabate had their first chance after just four minutes but sent a close-range header wide of the target.
Soon after, Benfica goalkeeper Artur Moraes did well to tip Nicolas Maurice-Belay's driven effort around the post and was alert again to divert another shot from the striker wide from the resulting corner.
Benfica's first opening did not come until the 21st minute when Cedric Carasso - whose unfortunate own goal in Portugal separated the two sides in the first leg - did well to block Rodrigo Moreno's close-range effort.
However, they led in the 29th minute when Jardel got up to meet Ola John's inswinging corner and head it beyond Carasso.
Now needing three goals, Bordeaux responded but Moraes pushed Diabate's shot away from danger and the Mali forward then missed the target before the break.
They continued to seek a way back into it after the break, but Diabate's header from Filho Mariano's free-kick did not have enough power to worry Benfica while Gregory Sertic's long-range shot floated over the crossbar.
They were given hope after 74 minutes when Henrique's long ball was knocked on for Diabate and he powered a shot into the top left-hand corner of the net.
But just seconds later, Benfica effectively killed the contest off when Nicolas Gaitan dinked a ball in from the left for Cardoza to finish.
There was still time for more goals even if the away-goal arithmetic was against Bordeaux.
The hosts would get one back in the last minute to level it on the night, with Jardel scoring an unfortunate own goal after Moraes' punch of Diabate's header struck him and went in - but again Benfica had an instant response as Cardoza lashed home a shot in stoppage time.