Benfica had a goal disallowed and hit the post in the first half, while Braga also came close with a dangerous long-range shot from left back Silvio.
The hosts went ahead five minutes after the break when Cardozo headed against the post and centre-back Jardel pounced to slide in from the rebound.
Braga levelled three minutes later when Hugo Viana sent in a curling free-kick from the left and an unmarked Vandinho headed in almost with his back to the goal.
Cardozo earned Benfica the win on 59 minutes with a powerful free-kick into the top-left corner that keeper Artur had no chance of making a save.
Benfica coach Jorge Jesus said he was confident the Lisbon side could reach a first European final for 21 years.
"I believe we are going to the Dublin final. We will be in for a tough game in the second leg but this game also gives us the confidence to go and defend the result in Braga," he said.
Braga coach Domingos Paciencia, whose team knocked out Liverpool and Dynamo Kiev among others to reach their first European semi-final, was optmistic that his side could overturn the first-leg deficit.
"This was not a good result but we know that everything is still up for grabs. In our stadium, in front of our fans it is going to be a different affair," he said.
"We know it is possible to beat Benfica at home and we have already given them a hard time over there before.
