Edinson Cavani glanced PSG ahead after 42 seconds and should have had a hat-trick before half-time, firing wide after rounding David Ospina before slipping to fluff a simple finish.
Sanchez rifled in Arsenal’s first shot on target with 13 minutes left.
Alex Iwobi might have had a late winner before Arsenal’s Olivier Giroud and PSG’s Marco Verratti were sent off.
Substitute Giroud was brought on to enliven a tame attacking display and picked up two yellow cards in his 27 minutes, the second for an altercation in which Italian midfielder Verratti also picked up a second yellow.
The Gunners were often exposed by the pace of Cavani, Angel di Maria and Serge Aurier and relied on their Colombian goalkeeper Ospina – preferred to Petr Cech – to keep them in it.
Iwobi’s low shot was tipped away by Alphonse Areola after Sanchez’s equaliser, while PSG would have had a 94th-minute winner had defender Marquinhos not wastefully headed wide from close range.