Leeds began to force their way back into the game after the half hour mark but threatened mainly from distance, though Matt Smith turned the ball on target from close range with Sam Johnstone claiming comfortably.
Rovers looked content to see the half out with patient possession, looking to ensure Leeds did not level things up.
They held onto the ball superbly as the half entered stoppage time before another breakthrough appeared almost by accident.
A missed tackle 25 yards out presented a clear path through to Sharp who took a touch, turned Sam Byram and somewhat scuffed a shot into the bottom corner past a wrong-footed Butland.
The introduction of Michael Tonge and Aidan White for Leeds at the break certainly made a difference as the hosts approached the second half with a level of vigour and intent they could only have dreamed of in the opening period.
Rovers themselves looked nervy over the first 15 minutes of the half and misplaced passes in midfield saw the pressure rarely abate.
But while they could not push Leeds back, Rovers defended superbly.
The introduction of Lucas Neill into the back four was seamless. Paul Quinn kept his place at centre half with Neill slotting in solidly at right back.
Abdoulaye Meite was particularly impressive in dealing with Smith as well as cutting out a series of final balls to deny chances for Leeds.
It was the turn of the hosts to claim for a penalty when James Husband appeared to handle in blocking a cross from the right but Bond was again unmoved.
For a side who defended so resolutely for the vast majority of the contest, there will have been some disappointment at the simple manner which Leeds pulled their goal back just after the hour.
A deep cross was headed back across goal by Matt Smith with McCormack rising unmarked to nod past Johnstone.
Leeds had their way back in but Rovers were not about to open the door again. They stood firm in front of everything the hosts had to throw at them.
Coppinger even went close to securing the win when he ran on to a loose ball but lashed it well over the bar.
The most nervy moment came deep in the second half and there was a sense Rovers dodged a bullet.
Johnstone raced out of his area to charge down McCormack who knocked the ball past him. The keeper then pulled McCormack back and referee Darren Bond blew his whistle. After a prolonged period of protests from both sets of players, Bond flashed a yellow card.
Leeds failed to produce a clear cut chance of an equaliser until deep into stoppage time when Smith met a chipped cross from McCormack but sent his header over the bar.
They may well have been forced to hold on but there could be few arguments that Rovers deserved the three points.
Such a performance deserved the biggest of fist pumps.