The former Barcelona forward had his side in front just a minute after the first-half break. Six minutes later, Alfonso Pedraza doubled the hosts’ lead.
With 15 minutes left to play, Leganes started their resurgence after Gabriel slotted from the spot.
On the stroke of full time, Joseba Zaldua completed the visitors’ comeback few minutes after Rodrigo Ely’s was sent off for a second bookable offence.
Munir has now scored four goals in the 18 league appearances he has made for Abelardo Fernández’s side this season.
Alaves are placed 16th in the Spanish top-flight log after collecting 19 points from 20 matches.
On January 28, the 22-year-old Spanish-Moroccan will face his former club Barcelona at the Camp Nou in their next league encounter.