Mahmoud Al-Amna (43rd minute) opened scoring for Aizawl and Lalthakima (56th) doubled the lead before drama unfolded at the Guru Nanak Stadium.
Loveday (61st) pulled one back for Minerva after the hour-mark and Kareem Nurain (81st) levelled the scoreline.
In the first half, Minerva Punjab had more possession of the ball and Aizawl FC struggled to capitalise on their opposition's follies.
Aizawl brought in their Under-22 player Lalthamika in place of Kingsley who is undergoing suspension at the moment. Aizawl broke the deadlock in the first half after Jayesh's through ball found Al-Amna who slotted home the goal for the visitors.
Also Read
Aizawl utilised their set pieces well from their dead ball specialist Jayesh Rane and found Kamo Bayi who made no mistake to put the ball past the Minerva Custodian Arnab Das.
Minerva came back into the game in the last quarter after Kareem's set piece was put into the goal by Loveday leaving Albino Gomes stranded.
Minutes later, Kareem scored a brilliant free-kick to deny the visitors three points.
Following the draw, Aizawl FC have 30 points from 14 matches whereas Minerva Punjab FC have 12 points from equal number of matches.
Disclaimer: No Business Standard Journalist was involved in creation of this content