Bayern progressed to the last four for the seventh time in nine seasons as they prevailed 2-1 on aggregate following their first-leg victory in Spain last week.
Sevilla's bid for a first semi-final appearance fell short in spite of shutting out Bayern's attack and restricting the hosts to just 51 percent possession.
"I'm proud of my team, they showed great personality and character against a very strong opponent, it wasn't easy," said Sevilla boss Vincenzo Montella.
"We can be proud of what we've done here, and all throughout this Champions League."
The Spaniards' defence constantly thwarted Robert Lewandowski, who was unable to add to his 35 goals this season, although Bayern had twice as many shots on goal.
Sevilla finished a man down after Joaquin Correa, who had earlier hit the crossbar, was sent off in the closing stages for a clumsy foul on Javi Martinez.
After Barcelona and Manchester City -- the runaway leaders in Spain and England respectively -- crashed out on Tuesday, Bayern are the only team left in Europe who can still win the treble.