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.
Arturo Vidal threatened on numerous occasions for the hosts in the first half, while Andrea Pirlo and Carlos Tevez went close after the interval and Pablo Daniel Osvaldo had a late goal ruled out for offside.
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.
Mirko Vucinic and Lazar Markovic, neither of whom were on the field at the time, were sent off after a touchline melee in a frantic finale that saw Juve, who remain on course to defend their Italian crown, suffer frustration.
Maxi Pereira was needed to shrug Paul Pogba off the ball inside the area after seven minutes, prior to Jan Oblak tipping a strike from Pirlo over the crossbar.
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.
The visitors looked lively on the break but failed to test Gianluigi Buffon, while Tevez volleyed over at the other end before the half-hour mark.
Vidal then threatened with two headers, the second of which was cleared off the line by Luisao as Benfica retained their slender advantage heading into the interval.
Rodrigo fired over the first effort of the second half for the visitors before Pirlo's free-kick forced Oblak into another smart save.
What could have been the turning point came 67 minutes in when Perez was shown a second yellow card for a late challenge on Vidal, yet Benfica held firm.
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.
Unused Juve substitute Vucinic and Markovic, who had just been hauled off by Benfica, were both sent off following a scuffle on the touchline.
Markovic and Perez are therefore set to miss the final against Sevilla, while Eduardo Salvio will also be suspended after picking up a late booking for handball.
