Mbappe plundered a stunning hat-trick to help Mauricio Pochettino's side to a 4-1 first-leg win at Camp Nou last month and the World Cup winner opened the scoring in Paris, whipping home from the penalty spot shortly after the half-hour mark.
That goal saw him overtake Lionel Messi as the youngest player to reach 25 goals in the competition, aged 22 years and 80 days, but the Barca talisman had his say soon after, thundering home a glorious equalizer from outside the area.
Barca's hopes of becoming the first side in Champions League history to progress from a knockout tie after losing the first leg at home by a margin of three goals evaporated before the interval when Navas kept out Messi's penalty, PSG seeing out the second half with the minimum of fuss to seal a 5-2 aggregate triumph.
Ousmane Dembele was guilty of squandering a number of fine opportunities inside the opening 20 minutes as Barca started on the front foot.
Keylor Navas tipped Sergino Dest's powerful drive onto the crossbar before Mbappe gave the hosts an undeserved lead after 31 minutes, the France international powering home from the spot after Clement Lenglet had tripped Mauro Icardi.
However, Messi pulled Barca level soon after with a stunning 25-yard strike into Navas' top-right corner – only Cristiano Ronaldo (20) has scored more Champions League goals from outside the area than the Argentinian's 19.
LIONEL MESSI. FROM WAY DOWNTOWN. 🚀 pic.twitter.com/PGkivnnZb7— Champions League on CBS Sports (@UCLonCBSSports) March 10, 2021
Messi should have added a second before half-time after Layvin Kurzawa had fouled Antoine Griezmann in the area, but Navas repelled his spot-kick – his first miss from 12 yards since February 2015.
A superb tackle from Marquinhos prevented Messi scoring from close range shortly after the hour mark, while Navas kept out Sergio Busquets' header at his near post.
Mbappe blazed over after a surging run in the closing stages, but it mattered little in the end as last year's beaten finalists booked their place in the quarter-finals in style.