In a sterling display at the Yuba Bharati Krirangan (YBK) here, United's Brazilian duo of Joshimar (67th and 70th) and new recruit Edmilson (33rd) brought the Bagan downfall and helped their side collect three full points from the match.
Bagan, however, did not give up without a fight and reduced the margin through medios Marcos Pereira (15th) Rakesh Masih (74th).
From the start of the match, nothing went right for the Karim Bencherifa-side as they suffered an early jolt when ace Brazilian striker Jose Ramirez Barreto had to leave the field with a muscle pull in the 24th minute.
Young Branco Cardozo replaced Barreto to pair up with Nigerian Edeh Chidi, who had a bad day at office, missing a number of sitters.
If that was not enough, India player Surkumar Singh was shown the red card in the 42nd minute after he hit out at Gouranga Biswas.
In their last meeting also -- in the Shield semifinal that Bagan won in penalty shootout on September 9 --green-and-maroon brigade was reduced to 10 men after Chidi was shown the marching order for head butting United's Eduardo.
With an off-day in office for Chidi, Pereira gave Bagan the lead from a James Singh corner.
Chidi missed a glorious chance as his shot went out after being deflected by Eduardo to earn Bagan a corner and then a brilliantly placed Pereira put the ball past United goalkeeper Sandip Nandy to make it 1-0 in the 15th minute.
The Subrata Bhattacharya-coached United earned a penalty in the 31st minute when Edmilson was brought down by Bagan goalkeeper Sangram Mukherjee inside the box.
Having signed up for United after he was sacked by East Bengal, Edmilson brought the equaliser by converting the penalty as both the teams went into the halftime locked at 1-1.
After the changeover, Bagan sorely missed Barreto as Chidi's lacklustre display did not go down well with an inexperienced Branco.
Surkumar's absence compounded Bagan's problem as United were successful in exploiting their opponent's defence.
Joshimar took a cross from right and beat Sangram in an aerial battle to head it home and give his side a 2-1 lead.
The Brazilian completed his brace three minutes later when he beat Bagan defenders to give United a 3-1 lead.
Bagan, however, reduced the margin when Masih utilised a Pereira cross to the fullest to score past Nandy.
Chidi got another chance in the fag end of the match, but only to see his volley go over the bar to see Bagan start their I-League campaign on a losing note.