However, they were forced to cling on for the win after cruising into a three-goal lead, only to be pegged back by two late strikes but managed to prevent the unlikeliest of comebacks to bounce back from their first defeat in six against Watford in their previous encounter.
Palace began in fine fettle and found themselves ahead on 20 minutes when they switched the ball from the left flank to the right via Brandon Aveiro, David Boateng and Sean Robertson, who delivered a pinpoint delivery into the box for James Daly to power home a header.
That advantage was doubled 17 minutes later when Joseph Hungbo forced the Coventry keeper into a save to force a corner, and some slack marking allowed it to be played short to an unmarked Aveiro. After his centre was fumbled by the shot-stopper, Kyle Lynch was on hand to simply tap home from a couple of yards out.
Things got even better eight minutes after the restart when Andrew Demby muscled his way onto the ball in a dangerous area and released Hungbo, who continued his fine campaign by netting with the outside of his foot from the edge of the box, moving him into double figures for the season and seemingly all-but secure the victory.
However, when Coventry captain Luke Rowe bent a superb 25-yarder around Oliver Webber that clipped the post on its way in on 88 minutes it looked to be a mere consolation, but in stoppage-time Costelus Lautaru lashed home from 12 yards after the ball was cut back into his path to set up a grandstand finish.
Despite the late scare McCarthy's team saw out the final few minutes to clinch yet another win and move into 2018 in firm control of the division.
Palace: Webber, Ossai, Hanson, Lynch, Mitchell, Boateng (Demby 42), Robertson, Aveiro, Oddy (Malcolm 60), Hungbo, Daly (Donkin 67). Subs not used: Funnell, Jno Baptiste.