Jimmy Smith's sixth goal of the season helped Rangers to their second win in a row in an open game at the Ricoh Arena.
Smith's scrambled second-half winner was one of the only highlights of the game in which both sides failed to create many chances.
Both teams had struggled to get shots on target in a drab first half.
Rangers had their only chance of the half after five minutes when Adam Bolder blasted wide from 20 yards.
The Sky Blues had their first attempt a minute later after a blocked shot from Dele Adebola fell to Khalilou Fadiga who had time and space eight yards from goal. But the former Senegal international saw his tame shot tipped away by Lee Camp for a corner.
Coventry's best chance of the game came on 28 minutes when a through ball from Andy Whing put Michael Mifsud clear. Camp produced a great double block first to stop the Malta striker and then Adam Virgo as he tried to cross the loose ball into the box.
The breakthrough came seven minutes after the restart when Coventry's poor defending gave Rangers multiple chances to take the lead.
Bolder's cross into the box led to a goalmouth scramble. Paul Furlong's strike from ten yards was blocked by Coventry goalkeeper Andy Marshall only for the ball to fall into the path of Stefan Moore.
His follow-up shot produced another superb save from Marshall who knocked the ball on to the post, but it was third time lucky for Rangers and Smith hammered the ball home to make it 1-0.
Iain Dowie brought on Leon McKenzie and Kevin Kyle to try and get back into the game, but Rangers were happy to defend for the majority of the second half to secure their fifth away victory of the season.