Sanju Pradhan (6') had put the visitors in front early in the first half but the slender lead was cancelled after Givson Singh (90+3') converted a late penalty.
Although the result kept the Warriors second with 23 points from 15 matches, three clear of third-placed Churchill Brothers, they now remain 12 points adrift leaders Mohun Bagan. The Arrows rooted at the bottom with nine points from 15 games.
Shanmugam Venkatesh heavily rotated his squad as only five players retained their place in the first 11 after the 2-0 loss against Chennai City last Friday. In came Ajin Tom, Hendry Antonay, Saurabh Meher, Ayush Adhikari, Gurkirat Singh and Harmanpreet Singh.
With Sergio Barboza suspended for the tie, Punjab coach Yan Law made three changes from his side that drew 1-1 at Gokulam Kerala with Anwar Ali, Thoiba Singh and Bali Gagandeep making their way in.
The tone of the match was set by a direct free-kick converted by Punjab skipper Pradhan in the sixth minute although with a bit of luck as Mitra misjudged his punch. The home side was also hit by an injury blow to Gurkirat who had to be replaced by Aman Chetri in the 22nd minute.
Chetri almost made an impact 10 minutes in but his shot would come off the upright while a suicidal backpass by Ali nearly saw Harmanpreet pounce on the same but for an alert Kiran Chemzong in the Punjab goal in the 51st minute.
Despite missing an influential figure in Vikram Singh, who was not named in the matchday squad, the Arrows kept piling the pressure and it finally paid off at the death.
Ali's foul on substitute Manvir Singh in the box in injury time allowed Givson convert from the resultant penalty that won the all-Indian side a point.