Trailing 1-0 from the first leg in Turkey, the hosts got off to the perfect start at the Estadio da Luz when Nicolas Gaitan put them ahead on the night and level overall within nine minutes.
They were pegged back by a Dirk Kuyt penalty against the run of play soon after, but Cardozo's slick finish restored Benfica's lead before the break and the Paraguay striker was in the right place again midway through the second half to slam home the crucial third goal and secure a 15th May final against Chelsea in Amsterdam.
Benfica headed into the game unbeaten in 13 home games and showed their attacking intent from the outset, taking a deserved early lead.
The Fener defence appealed optimistically for offside against Rodrigo Lima, whose clever cross set up Gaitan for a neat dink with the outside of his left foot which nestled in the net via the post.
Jorge Jesus' side continued on the front foot, but were stunned midway through the first half when French referee Stephane Lannoy pointed to the spot for handball against Benfica defender Ezequiel Garay.
The former Real Madrid man did not seem to know much about it as the ball flicked off his arm, but Kuyt showed no mercy and calmly despatched his penalty into the bottom-left corner.
The equaliser took the wind out of the hosts' sails and, understandably, boosted Fener.
Moussa Sow, leading the line in the absence of the suspended Pierre Webo, saw a decent effort from a tight angle saved by Artur and then dragged a shot wide after springing the offside trap.
The Portuguese league leaders were beginning to cut frustrated figures, appealing in vain for two penalties in quick succession, but 10 minutes before the break they went 2-1 up.
A quick free-kick found Cardozo, who worked himself some space on the edge of the area before unleashing a low left-footed drive past Volkan Demirel.
Kuyt could have grabbed a second crucial away goal soon after, but snatched at his angled shot and found only the side-netting.
With all to play for after the interval, it was the hosts who continued to muster the better of the chances - albeit without overly threatening Artur's goal in the early stages.
There was a lengthy delay around the hour mark after Gokhan Gonul bravely got his head in the way as Gaitan attempted a powerful left-footed volley, the Fener defender lying motionless for several minutes before being carried off on a stretcher.
It got worse for the Turkish side soon five minutes later, when Cardozo put Benfica 3-1 ahead on the night. Luisao's effort fell kindly at the feet of the Paraguayan, who controlled well before firing into the bottom-right corner from eight yards.
Benfica could and should have put the tie to bed soon after when Lima burst through down the left, but the Brazilian selfishly opted to shoot from a tight angle rather and was denied by Demirel.The tie remained on a knife-edge with the visitors knowing one goal would see them through to the final, but Artur was more than equal to whatever Fener threw at him as Benfica saw out the remainder of the game relatively untroubled.
|2||1st Half Goals||1|
|7||Shots on Target||4|
|6||Shots off Target||5|
|66.4||1st Half Poss.||33.6|
|63.4||2nd Half Poss.||36.6|