William Opoku Asiedu scored the decisive goal in the 16th minute and the Punjab-based outfit held on to the advantage till the end.
Minerva thus became the first team from Punjab to win the title since the 1996-97 season when now defunct JCT claimed the inaugural National Football League (NFL), which was later re-christened as the I-League.
Minerva finished their campaign with 35 points from their full quota of 18 matches.
Top division debutants Neroca FC finished at the second spot with 32 points following a 1-1 draw with East Bengal in Kolkata.
Mohun Bagan meanwhile, took the third spot with 31 points after being held 1-1 by a spirited Gokulam Kerala FC in Kozhikode.
Mohun Bagan have accumulated the same number of points as East Bengal, but sit one spot above their arch-rivals due to a better head-to-head record courtesy their wins in both legs of the Kolkata derby.
Mohun Bagan striker Asier Pierrick Dipanda Dicka finished as the highest scorer this season with 13 goals to his name.
Two-time champions Churchill Brothers, meanwhile, have been relegated. They finished second from bottom in the 10-team league ladder with a mere 17 points from their 18 matches.
All three matches kicked off at the same time at three different venues.
Chencho almost scored the opening goal in the eighth minute. A low cross from Khosla wasn't dealt with properly by Monday Osagie which gave Chencho a chance but he couldn't make full use of it.
The decisive goal came when William converted from point blank range after a rebound from Girik's shot.
The second half started with a flurry of attacks from Churchill Brothers but they were let down by poor finishing.
Minerva should have doubled their lead in 64th minute when Kassim played one two with Chencho but Chencho's following cross towards Sangwan, who was unmarked, went out for a goal kick.
Both teams failed to created clear chances in the final minutes as the local fans celebrated a historic triumph.
Meanwhile in Kolkata, East Bengal saw their heroic attempt to win their maiden I-League title come to a tearful end.
Felix Chidi (42nd minute) gave Neroca the lead shortly before half-time while Dudu Omagbemi (73rd) found the equaliser for East Bengal late in the second half.
However, it was of no avail for the hosts in the end. East Bengal needed to beat Neroca and then hope table-toppers Minerva Punjab don't triumph against Churchill Brothers.
Arch-rivals Mohun Bagan also had to not win at Gokulam Kerala FC as they have a better head-to-head record against East Bengal.
The first chance of the match fell to Neroca when Subash Singh dribbled inside the box but his meek effort was easily collected by East Bengal keeper Ubaid C.K.
At the other end, Syrian midfielder Mahmoud Al Amnah found the side-netting after Yusa Katsumi set him up from a short free-kick.
East Bengal then got three gilt-edged chances but Dudu spurned couple of them while Justin put too much on the shot with a wide-open net in front of him.
Neroca punished East Bengal for their wastefulness in front of goal when Chidi outfoxed Arnab Mondal inside the penalty area after being fed by Australian Nick Ward.
Just after the break, East Bengal appealed for a penalty when Dudu's shot struck the hand of a Neroca defender, but referee Rowan Arumughan waved play on.
Dudu then came close to equalising but smashed wide of the far post. The 32-year old finally atoned for his flurry of misses by heading in Lalram Chullova's cross after the hosts exchanged four passes.
Mohun Bagan meanwhile, needed to beat Gokulam in Kozhikode and hope for a slip-up by Minerva in order to lay their hands on the trophy.
They were off to promising start and created several chances in the early stages.
The Gokulam defence finally cracked under the relentless pressure when Arijit Bagui raced down the right wing to find Watson inside the penalty area.
Watson's shot came off the crossbar and Dicka punished the Gokulam defenders for their failure to clear the ball with some excellent dribbling skills and a fine finish.
But the celebrations of the Mohun Bagan fans was destined to be shortlived as the hosts found the equaliser during first half injury time.
Mohun Bagan continued with their attacking approach in the second half with Gokulam content to defend and hit back occasionally on the counter.
Although Gokulam created a couple of promising chances towards the end, the decisive goal eluded both teams.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)