Josh Sargent and Jovon Makama were on target as Norwich boosted their survival hopes with a first away win under Philippe Clement.
Sargent converted Matej Jurasek’s cross in the opening minute of the second half to lift the Canaries within a point of safety.
The visitors controlled the second period against a jaded Rangers side and might have increased their lead when substitute Makama was foiled by Paul Nardi.
But the young forward made it 2-0 in added time and, although Amadou Mbengue replied with a late consolation, it was not enough to deny Norwich their victory.
More follows.