The newly crowned German champions, who won their past two home games 6-0, needed defensive grit to match their usual attacking flair at a sold-out Allianz Arena.
Sevilla defender Joaquin Correa, who was sent off in stoppage time, hit the bar with a header and midfielder Pablo Sarabia, who scored in the first leg, wasted a glorious first-half chance.
But Bayern top-scorer Robert Lewandowski had a header pushed over the crossbar by goalkeeper David Soria and a brilliant block from Sevilla’s Jesus Navas denied Franck Ribery.
It was the first time in 22 home Champions League matches that Bayern had failed to score.
Sevilla defender Gabriel Mercado, replacing injured centre-back Simon Kjaer, was lucky to stay on the pitch after bringing down Lewandowski when he split the visiting defence in the second minute.
But Vincenzo Montella’s side recovered to control the first half, even if they were ultimately frustrated, none more so than Correa, who slid in wildly on Javi Martinez to earn a red card.
Bayern – into the semi-finals for the seventh time in nine years – join Liverpool, Roma and Real Madrid in the draw, which takes place in Nyon at 12:00 BST on Friday.
