Morris scored twice in the first half and once in the second as the Canaries stormed to an impressive win on Merseyside.
Jacob Murphy was also on the scoresheet for Norwich, while Everton’s Chris Long netted a brace.
Both sides had chances to open the scoring, with Long threatening early on for the hosts.
However, it was Norwich who took the lead after 14 minutes when Morris met Joshua Murphy’s cross and converted from close-range.
Everton responded well – Jonjoe Kenny saw his header narrowly creep over the bar – but Norwich doubled their advantage moments after the half-hour mark.
Murphy played provider again as he fed Morris and he calmly lifted the ball over the onrushing Mason Springthorpe.
But the home side gave themselves a fighting chance of getting back into the game when Long slammed the ball home from inside the box seven minutes before the interval to halve the deficit.
Unfortunately for the Toffees, Norwich’s two-goal advantage was restored in the 53rd minute when Springthorpe parried Murphy’s long-range shot into the path of Morris, who had the easiest of finishes to complete his hat-trick.
And Everton’s evening became even more difficult in the 61st minute when Ibou Touray was dismissed for a late challenge on Cameron Norman.
Despite Norwich’s numerical advantage, Everton again cut the deficit to one goal when Long netted from close range.
However, Norwich sealed the win nine minutes from time when Josh Murphy played in his namesake Jacob Murphy, who coolly slotted into the back of the net.