One of Europe's biggest spenders, but also one of the continent's most high-profile underachievers on the grandest stage, PSG finally seized their opportunity courtesy of goals from Marquinhos, Angel di Maria and Juan Bernat.
The former, who scored the first of two late goals in a comeback win over Atalanta in the last eight, rose to head home a superbly delivered free-kick from Di Maria.
The Argentine forward then finished well from close range following an audacious flick from Neymar after Leipzig goalkeeper Peter Gulacsi had relinquished possession with a dire kick.