Returning to action in the I-League a week after their violence-marred derby, the last year's runners-up looked out of sorts as the Nigerian forward of the rival team scored from an angular header in the 75th minute to hand the side full points.
United climbed to fifth place with 17 points from 11 matches, while East Bengal (21) remained on third with the result of their derby clash against Mohun Bagan yet to be announced.
It was an unlike display by the East Bengal forward line with Ishfaq Ahmed putting up a pathetic display while Edeh Chidi up front did not get enough support from Manandeep Singh.
Having missed a few chances, Ishfaq was substituted by Lalrindika Ralte but the damage had been done by then with United SC leading by Ranty's delightful header.
East Bengal defender Uga Okpara misread a Lalkamal Bhowmick corner as Ranty finished it with an angular header beyond Gurpreet Singh's reach.
In sharp contrast to East Bengal, United SC showed great ball control with Carlos Hernandez supplying from behind.
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East Bengal had an early chance to go one up when Chidi was brilliantly set up by Mehtab Hossain to be in a one on one with the rival goalkeeper Subrata Paul but his shot went off-target.
United had their first chance midway into the first-half when Hernandez plucked the ball from the air showing great control to set it up for Ranty but the Nigerian forward's booming shot from far was thwarted by Gurpreet.
There were more opportunities after the break and Ishfaq committed a harakiri of sorts when he was darting in the box and almost had a shot, but a great clearance from rival captain Deepak Mondal saw their scoreline remain intact.