The on-loan striker moved into double figures for the season as he scored in both halves after John Fleck had put Mark Robins' men ahead in the ninth minute with a low left-footed shot that went between two defenders and deceived goalkeeper Paul Jones.
It was a deserved lead, but Coventry had goalkeeper Joe Murphy to thank for maintaining their lead as the Irishman denied Crawley's lively midfielder Billy Clarke three times.
McGoldrick notched his 10th goal since joining Coventry on a temporary basis from Nottingham Forest right on the stroke of half time when he slid home Fleck's cross from six yards.
Coventry must have expected a reaction from Crawley and it came in the second half when Clarke took advantage of some scrappy defending and guided the ball home from just inside the penalty area.
But McGoldrick was on hand to relieve the growing pressure when he curled a right-footed shot past Jones in the 65th minute.