Zenit seemed content to sit on their 3-2 first-leg lead at Estadio da Luz, but had little to offer when Pereira's strike on the stroke of half-time swung the pendulum in Benfica's favour via the away goals rule.
The second period was more likely to produce a second for the hosts than an equaliser which would have put Luciano Spalletti's side back on course, but it did not come until the dying embers of the half when 20-year-old substitute Oliveira produced a calm finish to Bruno Cesar's through pass.
Jorge Jesus's troops advance to the last eight of the competition, something Benfica had not accomplished for six years prior.
The Portuguese side’s task was made apparent in the early stages of the second leg, with everything they threw at the Russian club being withstood and hacked clear.
It took a fantastic parry from goalkeeper Vyacheslav Malafeev to keep out Bruno Cesar’s curling effort from an angle on the right-hand side of the box 14 minutes in, moments before he was barged down on the edge of the area by Sergei Semak.
Unbelievably, the midfielder was told to get back up by referee Howard Webb, though it was unclear whether it would have been a penalty or a free-kick.
Benfica stopper Artur almost fluffed his lines two minutes before the interval when he came off his line to try and cut out a through ball, but his defenders held fort well to prevent the visitors having sight of an open goal in which to capitalise.
And three minutes later, the Eagles made the breakthrough when Cesar’s ball inside from the right picked out Axel Witsel, who after having a shot blocked by Malafeev was able to back-heel the rebound into the path of Pereira for the opening goal.
Of all the times for Zenit to lose their stranglehold on the tie, the strike could have come at a far worse moment. With a half-time talk from Spalletti to come soon afterward, the away side had 45 minutes to change their approach and look for the goal which would take them through.
But instead, the Russian club barely offered a threat to Artur’s goal and were lucky Jardel’s free header from a corner on 56 minutes did not punish poor defending.
Oscar Cardozo really should have wrapped things up with 20 minutes to go when clean through on goal just inside the area, only to suffer from heavy defensive pressure and send his low shot wide of the far post.
The striker did better five minutes later inside the ‘D’ after collecting a Cesar square pass from the left, forcing Malafeev to tip over his own crossbar, but was left frustrated at the resulting corner when an alleged shirt pull by market Tomas Hubocan went unnoticed.
With the result appearing safe as the seconds ticked away, Benfica finally made absolutely sure in the third minute of four added on at the end of the game.
Another counter-attack from further fruitless Zenit approach play saw the excellent Cesar stride down the right channel before meeting the run of Oliveira perfectly with his gentle through ball into the danger zone.
The young striker’s deft lifted finish over the committed Malafeev bounced inside the far upright and confirmed the Portuguese outfit’s passage into the quarter-finals.