A stunned Bayern found themselves 2-0 down after 28 minutes at the Allianz Arena as Paul Pogba and Juan Cuadrado struck for the Italians.
But just like in the first leg in Turin, when Bayern threw away a two-goal lead in a 2-2 draw, the hosts fought back as Robert Lewandowski netted on 73 minutes before Thomas Mueller's dramatic equaliser in the 91st minute forced extra time.
Thiago came off the bench to put Bayern ahead for the first time on 108 minutes before fellow replacement Coman -- on loan from Juventus -- curled in a superb strike on 110 minutes to put the Bavarians in the quarter-finals for the fifth season in a row.
This is the seventh time Guardiola has reached the Champions League quarter-finals in as many attempts as a coach at the highest level.
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In his four years with Barcelona, he won the title in 2009 and 2011, reaching the semi-finals in 2010 and 2012, while he steered Bayern to the last four in Europe in each of the last two seasons.
Much had been made in the build-up about how vulnerable Bayern are on the counter-attack and Guardiola's side were again found wanting on the break early on as Juventus went ahead with just five minutes gone.
Alvaro Morata then put the ball in Bayern's net after chipping Neuer on 22 minutes, but was wrongly flagged offside.
However, the Spaniard set up Juve's second by evading several Bayern defenders on a stunning run from deep in his own half, before finding Cuadrado in space. The Colombian kept his cool to fire past Neuer and leave Bayern with a mountain to climb.
Bayern pulled a goal back when Douglas Costa's cross from the right was headed home at the back post by Lewandowski, then Coman swung in the cross for Mueller to head home the equaliser.
A superb save from Neuer denied Lichtsteiner early in extra time, but Bayern were not to be robbed of a famous comeback victory.
Thiago was brought on for Franck Ribery and quickly made an impact as he played a one-two with Mueller before guiding the ball into the bottom corner with a superb finish.