Top scorer Cardozo, who signed a new deal in January and has a 60 million euros buyout clause in his contract, proved too hot to handle after Dirk Kuyt's away goal had given Fenerbahce the upper hand.
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Benfica, last in a continental final in 1990 when the Portuguese lost to AC Milan in the European Cup showpiece, took just nine minutes to cancel out Fenerbahce's 1-0 lead from the first leg when Nicolas Gaitan clipped in Lima's low cross.
Cardozo's fine left-foot finish restored Benfica's lead on 35 minutes in a breathless first half and his decisive strike came on 66 with another crisp low shot from inside the area.
"This is historic given the last time Benfica got to a European final and we get there with all justice," Benfica coach Jorge Jesus told Portuguese television.
"Our dynamic was stronger, pace higher and we managed to keep it throughout the match because we kept the ball. They scored from a penalty but never really created a lot of problems."
Chelsea, last season's Champions League winners, beat FC Basel 3-1 at Stamford Bridge on Thursday to ease through 5-2.
Fenerbahce had struggled to stem the early onslaught but got an unexpected gift when the ball struck Garay's arm as he tried to clear and Kuyt coolly converted from the spot.
Cardozo put Benfica in the driving seat when Lusiao's shot fell into his path and the striker fired into the corner.
