Seasoned Cameroonian striker Dipanda Dicka gave the hosts the lead in the first half and they almost clinched a win, before young Subha Ghosh snatched an equaliser late in the second, to ensure it was honours even.
Bagan now have 14 points from seven games while Punjab moves one place up to second with 11 points from eight.
At the end of the game, Bagan's four-match winning streak was halted but Punjab managed to maintain what is now a seven-game unbeaten run.
The Kolkata giants were the more attacking off the blocks, but Punjab played the off-side trap to perfection to thwart any clear attacks on goal save a Fran Gonzalez effort early on.
Punjab, who had been working well on the set-pieces, then went ahead off a corner which was taken short by Sanju Pradhan from the right. Cavin Lobo then floated in a cross, dropping mid-way into the Bagan six-yard box. A lurking Dicka met it with a superb side-volley, body still in air and holding off a defender, all in one action. It wrong-footed and stunned Sankar Roy in the Bagan goal to give the hosts a valuable lead.
Spaniard Joseba Beitia shot over the bar from close in the 68th, while VP Suhair in the 70th also shot wide with only the keeper to beat. And when Bagan substitute and new foreign recruit Komron Tursunov of Tajikistan shot wide from close in the 85th, it looked all but over for the Green and Maroons.
However, the new Bagan sensation and young super-sub Subha Ghosh clearly had other ideas.
A Bagan foray into the Punjab box, dropped harmlessly and favourably for Teah Dennis to clear. Just as the Liberian defender was looking to do so, Subha who had been following play, crept up at pace from behind, snatched it from the toes of Dennis to get ahead and unleashed a right-footer along the ground which found its way through a bevy of defensive Punjab legs and across a diving Kiran Limbu in goal, to find the back of the Punjab net.
It was the talented Bagan youngster's third goal of his debut senior season, and all of them important goals in their own right.
Sankar Roy in-fact pulled off his third good save in what turned out to be the last kick of the game when Bali Gagandeep, who had come in place of Dicka in the second half, shot from close. It was heading towards goal but the keeper parried it well and it came off the Bagan upright.
( With inputs from IANS )