Chelsea and Arsenal will meet in the UEFA Europa League final after confirming a historic feat for the Premier League.
Kepa saved two spot-kicks as Chelsea won 4-3 on penalties after a 2-2 aggregate draw with Frankfurt.
Ruben Loftus-Cheek slotted in the Blues' opener at Stamford Bridge before Luka Jovic's strike forced extra-time.
After Cesar Azpilicueta's penalty miss, Kepa denied Martin Hinteregger and Goncalo Paciancia, to allow Hazard to set up a London derby in the final in Baku, Azerbaijan, on Wednesday 29 May.
See: Chelsea report
Aubameyang's treble inspired a 4-2 victory for Arsenal to seal a 7-3 aggregate triumph in Spain.
Kevin Gameiro put the home side in front on 11 minutes, but Aubameyang scored superbly from outside the area before Alexandre Lacazette put Arsenal 2-1 up five minutes after half-time.
Gameiro struck again eight minutes later but Aubameyang netted twice more to wrap up their victory on the night.
See: Arsenal report