Joe Willock's shot deflected in off Nketiah to put Arsenal ahead early on at Boreham Wood and Reiss Nelson showed brilliant footwork to double the lead.
Nketiah made it 3-0 from inside the area just past the hour and completed his treble 13 minutes from time.
The 18-year-old now has nine PL2 goals, one off the top scorers, Oliver McBurnie and Harry Wilson, who are now both out on loan.
Ramiro Funes Mori featured for the opening 45 minutes in his first appearance for Everton since March after injury.
Everton remain fifth.
Arsenal: 19 Feb v Leicester (A) PL2
Everton: 12 Feb v Barnsley (A) PL Cup