Castro Custodio's first-half header was sufficient to send Braga through on the away-goals rule as Vandinho's strike in the 2-1 first-leg defeat a week ago proved crucial.
The win sends Domingos Paciencia's troops through to an all-Portuguese final in Dublin on May 18, where Porto lie in wait after they completed a one-sided victory over Villarreal in tonight's other last-four encounter.
Should Braga upset the form book against the reigning Portuguese champions in just under a fortnight, it would secure the club their first major silverware since lifting the Portuguese Cup in 1966.
The opening to tonight's encounter was understandably cagey, with only Benfica defender Luisao's ninth-minute header from a corner forcing either goalkeeper into meaningful early action.
But the hosts were ahead on 18 minutes with a chance out of nothing.
Hugo Viana's corner dropped right on the edge of the six-yard-box and should have been dealt with by the visiting defence, but Custodio was allowed to rise unchallenged to thump home a great header.
Fabio Coentrao was making good inroads down the left for Benfica and he started the move which nearly led to the leveller four minutes before the break.
Coentrao broke forward and played the ball through for Oscar Cardozo, who squared the ball first time. Javier Saviola met the ball with a low left-footed effort but saw the ball come back off the upright. The rebound broke to Coentrao but he could do no more than blaze wastefully over.
Benfica started the second half on the front foot with Saviola looking to burrow his way through the home defence after getting the ball in a good position in the area, but Braga's backline cleared.
Just before the hour the visitors went agonisingly close when Franco Jara worked space 22 yards out and curled in a shot which just missed the angle of post and bar.
On 69 minutes Cardozo attempted a repeat of his exquisite free-kick that gave Benfica the edge coming into tonight's game, but on this occasion he could only fire harmlessly over.
Coentrao got in behind the Braga defence two minutes later but Artur was alert to the danger and cleared just a fraction of a second ahead of the Benfica winger.
And with 12 minutes remaining Artur kept his side ahead once again, this time making a good save going low to his right after Nicolas Gaitan connected sweetly with a half-volley on the edge of the area.
And from the resulting corner another chance went begging for an increasingly frantic Benfica, as Luisao's flick-on was bundled wide on the goal-line by Saviola, who in any case could have been hauled up for either handball or offside had he put the ball in the net.
Viana might have sealed the win for the hosts on 83 minutes but Roberto was equal to his effort from the edge of the box, as he was just 60 seconds later when he beat away Custodio's fierce drive.
Benfica almost snatched it with two minutes left but Braga were indebted to the smart positioning of Junior, who hacked the ball off the line to deny Alan Kardec's goalbound header.
Benfica threw everything they had at Braga in what time remained, but the hosts stood firm to register their eighth clean sheet in nine European games this season - which perhaps more than anything was the key to their remarkable run to the final.
