Whatever R's boss John Gregory said at half-time did wonders for the west Londoners, who struck three times to earn themselves a first win on their travels since November when they won at Cardiff.
First City failed to cope with a Marcus Bignot free-kick which Marc Nygaard nodded on for Inigo Idiakez to head home within just two minutes of the restart.
Then the Hoops were awarded a 51st minute penalty after Alan Maybury had bundled over Paul Furlong with Danish international Nygaard scoring low to the left with Paul Henderson going the wrong way.
And the Foxes' nightmare worsened on 68 minutes when Nygaard struck a glorious third by smashing a 30-yard drive from out on the right which flew over Henderson and into the top left-hand corner.
Deep in time added on at the end of the game, Iain Hume scored a consolation penalty for Leicester after Danny Cullip had handled inside the box.
It was almost a total contrast to the first half in which Rangers had failed to get a single effort on target.
Right on the stroke of half-time, Rangers were presented with a fantastic opportunity to take an undeserved lead when an unmarked Nygaard shot wide from eight yards when it had looked easier to score.
But within minutes of the restart there was to be a dramatic reversal of fortunes.
Leicester had been first to almost every ball in tackle and had done everything but score.
Up to that point, Rangers' man-of-the-match by a mile had been their goalkeeper Lee Camp, who was in inspired form and came to his side's rescue with quality stops to deny Maybury, Hume and Stephen Hughes.