PSG went into the second leg at the Parc des Princes with a 3-2 lead from last week's game at the Allianz Arena.
Neymar squandered a couple of good chances in the opening exchanges as Bayern pressed for the goals to bring them back into the tie.
And then the Brazilian was thwarted by the woodwork.
After a slick back heel eliminated Kingsley Coman, Neymar turned and saw Bayern goalkeeper Manuel Neuer off his line. His chip beat Neuer but struck the crossbar.
A minute later he hit the post after being set up by Mbappé.And in their next surge upfield Bayern took the lead. David Alaba's snap shot was straight at PSG goalkeeper Keylor Navas but the ball looped up and Eric Maxim Choupo-Moting rose higher than Presnel Kimpembe to nod in.
Misses
Neymar's woe continued after the pause. Angel Di Maria chested the ball down in the penalty area, took out Alphonso Davies and Neuer and rolled the ball across the six yard box but Neymar, sliding in, could not make contact.
Pochettino replaced Julian Draxler with Moise Kean to add some forward thrust and fresh legs. The Italy international could have grabbed the glory soon after his introduction but he slashed wildly at the ball and it sailed over the bar.
Bayern too were guilty of missing their chances. Leroy Sané found himself in space in the PSG penalty area in stoppage time. But though he had options, his cross went straight into the grateful arms of Navas.
PSG proceed on the away goals rule and will play the winners of Wednesday night's quarter-final between Manchester City and Borussia Dortmund.
City take a 2-1 lead into the second leg in Germany.
In Tuesday night's other match, Porto beat Chelsea 1-0 but go out 2-1 on aggregate. Chelsea will face either Real Madrid or Liverpool for a place in the final in Istanbul on 29 May.
