City were given the run around by an attack-minded Rovers side and seldom posed a threat themselves.
Westwood produced a series of fine saves to deny Doncaster the victory they deserved for a performance full of enterprise and attacking endeavour.
Coventry earned full marks for a spirited backs to the wall display in which central defenders Ben Turner and Martin Cranie turned in commanding performances as Rovers piled on the pressure.
Westwood set the pattern for the game when he came to the rescue to keep out an early shot from James Coppinger and was by far the busier of the two keepers for the rest of the game.
Try as they may, Rovers just could not make the breakthrough as the visitors held firm.
Dean Shiels dribbled into the box in the 21st minute but was denied a shot on goal by an old-fashioned shoulder barge by Stephen Wright which knocked him completely off the ball.
Doncaster's appeals for a penalty were waived aside by the referee but there was little respite for the hard-pressed visitors' defence.
Shiels raced clean through again four minutes later but fired straight at Westwood before Leon Best managed Coventry's only shot on target throughout the game with an angled effort that was palmed away by Neil Sullivan.
Westwood made a super save to tip a cracking free-kick from Brian Stock onto the post just before the interval and was busy again early in the second half.
The Irish keeper did well to parry efforts from Stock and Shiels in quick succession after Michael McIndoe had missed a great chance to pinch the points for City in the 59th minute with a weak shot straight at the keeper.
Doncaster kept up the pressure right to the final whistle but it was all to no avail as there was just no way past the in-form Westwood.