The two sides' previous meeting ended in a 4-1 Shrews success, but this was a closer affair as the sides traded opportunities throughout.
Coventry goalkeeper Joe Murphy denied Luke Rodgers after he exchanged passes with Matt Richards in the penalty area early on before home striker Gary McSheffrey rattled the crossbar from 25 yards.
Marvin Morgan twice went close for the visitors after good build-up play down the left, but could not apply the finish.
The hosts had the better opportunities in the second half, McSheffrey wasting the best of them when he missed the target after a poor backpass fell to him 15 yards from goal.
That miss was punished in the 62nd minute when Morgan tapped in from close range after Richards had seen his header acrobatically saved by Murphy.
Coventry's new signing Leon Clarke joined his side's attack and would have marked his debut with the equaliser, but for a goalline clearance by Richards.
The visitors held on after an incredible double save from Shrews goalkeeper Chris Weale thwarted McSheffrey and Clarke in the closing stages.