Costa Rican World Cupper Carlos Hernandez scored the all-important goal in the 89th minute to give United SC a winning start to the New Year and final phase of the I-League.
Dempo were reduced to 10 players in the 85th minute when their left back Debabrata Roy earned his second yellow card for a bad tackle to United SC midfielder Shankar Oraon.
Minutes later there was another bad tackle by Dempo to Hernandez just outside the box as referee awarded a freekick to the purple brigade. Hernandez scored a blinder from the free-kick to hand United their first victory in three matches.
The loss meant that Dempo have 26 points from 14 matches, while United SC shot up to top five with 21 from 14.
Dempo had a fine chance at the stroke of half-time when defender Rowilson Rodrigues' header from a Clifford Miranda cross went above the crosspiece as both the teams were locked in a goalless stalemate at the break.