It took just nine minutes for the visitors to make the breakthrough, Mandzukic firing home from close range after Northern Ireland goalkeeper Alan Mannus had palmed a Cop shot straight into the path of the Juventus forward.
Croatia continued to boss proceedings as the first period drew to a close, and they had their second 10 minutes before the break when Cop poked the ball home from close range after a smart header from Matej Mitrovic.
The scoring was then rounded off in the 67th minute when Kramaric picked up possession some 25 yards from goal before finding the top corner with an outstanding strike.
Northern Ireland, who are currently second in their 2018 World Cup qualifying group behind Germany, will return to competitive action with a Group C clash at home to Norway next March.
Meanwhile, Croatia, who top their qualification group ahead of Ukraine, will attempt to make it five wins in a row when they host Ukraine in March 2017.