Ranti Martins put the visitors ahead in the 12 minute but the host came back strong and equalised through Taro Hasegawa in the 33rd minute before Luciano Sobrosa scored from the spot in the 62nd minute.
The result allows Mohammedan Sporting to do the double over RUFC and move up a place to 12th in the ranking.
Rangdajied, meanwhile, drop to the 10th place as Mohun Bagan, by virtue of the point earned against United SC, accumulate 25 points to go up to 8th.
However, coming into the match today, it was Rangdajied which started the brighter of the two. David Ngaihte, who got a start after a long time, was into the thick of things right in the 2nd minute when his shot sailed wide off the far post.
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In the 5th minute, Elam Abocha did well from the midfield and tried to send in a through pass to Ranti which Luciano Sabrosa intercepted.
The attacks paid dividends in the 12th minute, when the Goal Machine - Ranti Martins - scored his 8th goal for Rangdajied.
It was David Ngaihte again from the right who outpaced a defender to send in a cross at the far post for Lalnunpuia to do the scoring. But Puia's header was saved by Luis Barreto on which Ranti pounced over and slotted the ball into the goal.