Palace made eight changes from Saturday and Coventry five and it was the visitors who started the brighter with Gary McSheffrey twice wasting good opportunities having slipped away from Fitz Hall.
It summed up Coventry's night as they only had one effort on target.
Other chances were all dispatched several rows behind the goal with McSheffrey the chief culprit.
That said he was Coventry's most potent threat as Palace failed to find much cohesion in a scrappy first half.
Wayne Andrews' quick feet created a couple of chances in the last five minutes of the half but he blazed wide from an angle before forcing Clayton Ince to make a save.
Palace improved after the break. Andrews was unlucky not to see either of two efforts in the 56th and 64th minutes go in - one curled round the left-hand post and the other the right both from the angle of the box.
Then came the moment that settled the match. Reich dispossessed Andy Impey on the left wing before running in and dispatching a superb shot into the top-right hand corner.
Palace's man of the match, Jobi McAnuff, nearly added a second two minutes later but shot at the keeper.
Andrews also came close when put through by the same player.
Coventry threw on all three substitutes in the last 20 minutes but the nearest they came to a leveller was when Claus Jorgensen fired across the six-yard box.