Jorge Jesus' men, beaten finalists against Chelsea last year, were able to shut out the Italian champions at the Juventus Stadium to book their place in the final, which will be held at the same venue on May 14.
Lima's late strike in Portugal last week handed Benfica a 2-1 lead ahead of the return leg. Although they failed to build on that advantage, a stubborn defensive performance denied Juventus as Benfica overcame the dismissal of Enzo Perez for a second bookable offence 23 minutes from time.
Perez's red card offered Juve fresh hope heading into the closing stages, but Benfica, whose own attacking threat was limited, called upon all their European experience to hold on and keep alive their hopes of a domestic and European quadruple amid more late dismissals.
Oblak had returned to Benfica's team in place of Artur and the goalkeeper was given a scare by Vidal soon after.
Vidal, who shook off a knee injury to make Juventus' starting line-up, came close to opening the scoring, only for his lobbed effort to nestle on the roof of the net.
Rodrigo fired over the first effort of the second half for the visitors before Pirlo's free-kick forced Oblak into another smart save.
Stephan Lichtsteiner's control let him down when he evaded the Benfica backline and Osvaldo looked to have scored, only for the strike to be ruled out for offside, before tempers flared.
