Bayern took the lead in the opening exchanges at the Allianz Arena, but were frustrated for the remainder of the game as Benfica limited the deficit to one going into next week's second leg in Lisbon.
The visitors went into the match as one of Europe's form teams with 19 wins from their last 20 games, but they fell behind inside two minutes when Vidal got in front of the defender to glance Juan Bernat's cross in from close range.
It was an ominous start from Pep Guardiola's men, and they threatened to add a second soon enough when Douglas Costa engineered space to shoot before testing Ederson with a low drive from the edge of the area.
The Brazilian was by far the busier of the two keepers, and needed to be alert to smother the ball at the feet of Robert Lewandowski after Costa had sent Philipp Lahm to the byline down the right channel.
Benfica did start to come back into the match as the first half progressed, and had a penalty shout shortly before the half-hour mark when Nicolas Gaitan's low cross struck the arm of Lahm before Eliseu blasted a follow-up effort over the crossbar.
It was still Bayern who looked most like scoring, though, and Vidal almost stole in for a second when another late run into the area saw him get between two defenders, only to plant his header into the ground and see it bounce back up over the crossbar.
Benfica continued to frustrate the hosts in the second half, and almost grabbed an all-important away goal shortly before the hour mark when Jonas flicked the ball past David Alaba only to fire his effort too close to Manuel Neuer when well placed.
Bayern immediately went up the other end and came close through Bernat, but they were once again fortunate not to be pegged back when Jonas missed two more presentable chances in quick succession - the best of which saw him plant his finish straight into the gut of Javi Martinez.
The hosts finally created their first real chance of the second half with less than 10 minutes remaining when Franck Ribery charged into the box from the left flank and forced Ederson into a save from a tight angle.
Bayern upped the tempo in search of a second goal during the closing stages of the match and saw one half-chance from Lewandowski nodded over the crossbar, but the Polish striker then squandered a sitter when he was played clean through on goal but overhit his pass to Lahm, who would have had an empty net to aim at.
Benfica held out against the late pressure to limit the home side to just the one goal, however, leaving them in a good position going into the second leg at the Stadium of Light next Wednesday.