The five-time European champions were made to dig deep prior to their breakthrough goal shortly before half time, though they went on to add four more goals to their tally ahead of next month's needless second leg.
Besiktas had given a good account of themselves prior to Domagoj Vida's dismissal early on, which Robert Lewandowski and Thomas Muller took advantage of by finding the net twice apiece at the Allianz Arena.
Knockout-stage debutants Besiktas, boasting an unbeaten record from their six group matches, made a bright start to the contest and looked particularly dangerous when key man Anderson Talisca got on the ball.
Any hope the visitors had of snatching a goal on the counter-attack faded as early as 16 minutes in, though, as Vida was shown a straight red for bringing down last man Lewandowski.
Up until that point the closest Bayern came to a breakthrough was via Kingsley Coman's curler, which was heading for the bottom corner if not for Fabricio's intervention, while Muller also sent a couple of headers wide.
Momentum was very much with the Bundesliga pacesetters from the moment Besiktas went down to 10 men, however, and Fabricio would be required again soon after to somehow keep out Lewandowski's header from point-blank range.
Besiktas did have their moments, coming close to taking a shock lead when Ricardo Quaresma got an angled shot on target for Sven Ulreich to push over the bar, but Bayern were ahead with a couple of minutes of the first half left to play.
Arturo Vidal had an attempt from the edge of the box easily dealt with and Lewandowski struck the post from a free kick soon after play resumed.
Lewandowski then played a pivotal role in Bayern's second goal of the evening, cutting the ball back for Coman right on the penalty spot for the French attacker to sweep past Fabricio.
The introduction of defender Dusko Tosic for striker Vagner Love signalled Senol Gunes's intent for the remaining half-hour of the contest - keep the score down and subsequently keep the tie alive ahead of the return match in Turkey three weeks from now.
That proved to be too much of an ask against a Bayern side with 14 wins in a row to their name in all competitions, as Muller flicked out a leg when left unmarked at the front post to convert Joshua Kimmich's cross and add a third.
Muller sent his next shot over the crossbar when seeking a hat-trick, and Coman could only pick out Fabricio as the Bayern onslaught continued.
The fourth would arrive 11 minutes from time, this time through Lewandowski after the striker reacted quickest to Mats Hummels's saved shot for a simple finish.
Besiktas's suffering was not over there, either, as moments after Fabricio had kept out Javi Martinez with a stunning save, Muller teed up Lewandowski to round off the scoring with another close-range finish.
BAYERN MUNICH (4-3-3): Ulreich; Alaba; Hummels, Boateng, Kimmich; Rodriguez (Robben 44'), Martinez, Vidal (Tolisso 83'); Coman (Ribery 81'), Lewandowski, Muller
BESIKTAS (4-2-3-1): Fabricio; Adriano, Pepe, Vida, Erkin (Gonul 69'); Quaresma, Medel (Arslan 85'); Hutchinson, Talisca, Babel; Love (Tosic 57')