The hosts had lost their opening encounter against Delhi Waveriders and needed a win to get their campaign on track.
However, despite a fare better display of possession hockey, they failed to dominate the opposition at the Surjeet Singh Stadium.
Rhinos' English recruit Ashley Jackson put the team ahead with a clinical drag flick in the 43rd minute and Mandeep Singh benefited from a defensive error on a hopeful cross from the right to score the second six minutes later.
Warriors looked to turn the match around in the fourth and final quarter as Aussie Kieran Govers managed to reduce the deficit with a reverse hit seven minutes from time.
However, that only proved to be a consolation goal as the Rhinos withered away the storm to pick five points from the encounter.
Earlier, both teams began on cautious note, unwilling to concede any quarter to the opposition in the midfield.
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The safety first approach meant that none of the teams were willing to commit more men forward and the entire first quarter did not see a single shot on goal from either side.
The best chance of the opening quarter fell to Ranchi Rhinos when their South African recruit Austin Smith earned them a penalty corner with some deft stick play in the 11th minute. However, the opportunity was wasted as they failed to collect the ball cleanly and the defenders had enough time to clear it to safety.
The hosts began pushing forward in the second quarter and managed to dominate possession but their first real chance for a goal came after the half an hour mark when Govers received an excellent diagonal pass from the right but he could not beat Rhinos goalkeeper Francisco Cortes at the near post. More