Sony Norde (43') opened the scoring and edged the visitors ahead. Moinuddin Khan (88') equalised for the Punjab-based side late in regulation time.
Minerva Punjab head coach Khagen Singh had a fully fit squad to choose from and started in a 4-3-3 formation. Arshdeep Singh was the goalkeeper with Deepak Devrani, Sukhdev Singh, Guy Eric Dano and Abhishek Ambedkar creating a defensive screen in front of him.
Kassim Aidara, Toshiya Hosoe and William Opoku made up a three-man foreign midfield. Bhutanese winger Chencho Gyeltshen was on the left flank with Gagandeep Bali on the other. Girik Khosla was the striker deployed up front.
Mohun Bagan in a classic 4-4-2 setup had Shilton Paul in between the sticks. Gurjinder Kumar and Ricky Lallawmawma, the full backs had Kinshuk Debnath and Kingsley Eze for company at the back. Raynier Fernandes started in central midfield alongside Shilton D'Silva to accommodate Chesterpaul Lyngdoh on the right flank.
Skipper Sony Norde and strikers Anusmana Kromah and Aser Pierrick Dipanda made sure the Bagan lineup had no shortage of stars even though the Indian contingent looked depleted, most favouring a move to the Indian Super League.
The visitors took a long time to get going as did the blue-stripped hosts. Much of the game was played in the midfield and neither side were unable to create serious intrusions into either's opposition box early on.
However, Chencho Gyeltshen did ask some questions which the shaky yet experienced Mariners' backline saw off easily. It had to be the Haitian magician who broke the deadlock to score the season's first goal.
Sony Norde, who quickly changed flanks was fed the ball in the midfield and with a brilliant solo effort, gushed into the box, beating three men and slotted the ball home, aiming for the far-post with only a couple of minutes to go for the halftime whistle.
Minerva came throttling down after the break and could have been two goals up, if not for damned luck and some atrocious shooting. Ushered in after the break, Ivorian Lago Dagbo Bei first hit the post and then set Girik Khosla up, the young Indian striker failing to convert from close space.
Even Deepak Devrani could have scored against his old club from point-blank range, but the defender chose to blast it over the bar.
Sanjoy Sen's side seemed happy with the one-goal cushion which would have sealed all three points but the real drama was left for late in the game. Sony Norde found space in front of him and fed the ball towards youngster Shaikh Faiaz but the substitute could not tap the ball in - the scoreline remaining the same with only ten minutes to go.
Captain Sukhdev Singh's flag-kick landed in between a host of players in front of 'keeper Shilton but the ball was played towards second-half substitute Moinuddin Khan who was left unmarked and the striker made no mistake in lodging the equaliser, triggering wild celebrations in the stadium.
There was no reply from the away side and the mighty Mohun Bagan had slumped to an away draw yet again - one of the reasons they fell a few points short to end runners-up last season.
For the Kolkata giants, it would have been a far from ideal preparation given they would be facing cross-city rivals in the derby next Sunday.