Yusif Yakubu gave an early lead in the fifth minute when he played a one-two with fellow striker Joshimar DSilva, with leaving the Arrows keeper Naveen Kumar with no chance.
The Arrows had a chance to equalise when C S Sabeeth missed an open header off a pass from Tirthankar Sarkar from the left.
But the AIFF developmental oufit found a 62nd minute equaliser with Prabir Das setting it up for Sabeeth who headed home.
The Arrows joy, however, lasted just three minutes as Malsawm Tulunga showed his class with a clever tap from Yakubus pass that foxed Naveen Kumar for the match-winning goal.
The Arrows resorted to counter attack resulting in a 77th minute strike from substitute Bikramjit Singh (Sr) but it hit the post.
The win helped United SC climb to seventh position with 38 points, while Arrows remained winless with eight points from 20 outings.