A 5-0 victory in last month's first leg in Munich had put Bayern in a commanding position and there was never any sign of a miraculous comeback in Istanbul.
Thiago finished from a Thomas Muller cross to extend Bayern's advantage and score its 100th goal of the season, but the Spain international was withdrawn before the break, coach Jupp Heynckes perhaps wishing he had rested more key names after picking a strong side.
Gokhan Gonul's own goal in the first minute of the second half appeared to settle the tie for good, before Vagner Love scrambled home his first UEFA Champions League strike since 2011 to spark Besiktas's best period of the tie.
Sandro Wagner, though, restored Bayern's two-goal cushion with his first strike in the competition in the 84th minute.
Heynckes's men could claim the Bundesliga title at the weekend if results go their way and they remain on track for another treble, the veteran coach having won the UEFA Champions League among three trophies before departing Bayern at the end of his third spell in 2013.
Bayern, which has reached the UEFA Champions League semi-finals in six of the past eight seasons, will find out its quarter-final opponent in Friday's draw.
Despite a massive first-leg lead Bayern made a bright start, Arturo Vidal heading wide.
Thomas Muller scored twice in last month's game and he should have opened the scoring in the 10th minute, blasting over the rebound after Tolga Zengin parried David Alaba's free-kick.
But Muller created a fine goal for Thiago to get Bayern up and running, the midfielder timing his run into the box perfectly to tuck away a first-time finish from a pinpoint right-wing cross.
Thiago limped off before half-time, giving Bayern an injury concern for the rest of the season.
Besiktas had played reasonably well in the first period but the Turkish champions gifted Bayern its second moments after the restart.
An innocuous right-wing cross from Rafinha should have been easy to clear, but Gonul poked the ball past Zengin under no pressure whatsoever.
Referee Michael Oliver then had to briefly pause the game as a cat invaded the pitch.
Besiktas gave its fans something to cheer in the 59th minute, Alaba losing the ball in his own half, with Gonul setting up Love to squeeze the ball past Jerome Boateng on the line.
Mustafa Pektemek forced a save from Sven Ulreich as Besiktas tried to level the game on the night, Bayern understandably lacking energy given its comfortable position.
Bayern made sure of the win on the night, though, substitute Wagner chesting home from close range with six minutes to go after Alaba's cross deflected up perfectly for him.