The striker, in fine goalscoring form for the Under-23s since returning from injury, scored the opener just after half-time.
He was then denied by a superb save from Max Strycek before heading in Pedro Chirivella's first-time cross on the hour mark.
Trent Alexander-Arnold added a third, twice beating his man before finishing with a powerful strike.
Jack Stephens netted the only goal, heading Callum Slattery's free-kick in off the crossbar on 38 minutes.
Harley Willard was denied by Spurs goalkeeper Tom Glover on the stroke of half-time, before Southampton shot-stopper Harry Lewis saved efforts from Kyle Walker-Peters and Reo Griffiths as the visitors pressed for a leveller.
Both teams finished with 10 men as Willard and Spurs' George Marsh received second bookings after an altercation.
Chelsea's Charlie Wakefield levelled on the hour after Reiss Nelson's opener for the Gunners at Stamford Bridge, but Stephy Mavididi won the contest on 82 minutes with a fine solo goal.
That was a second win of the season for promoted Division 1 side Arsenal, who are two points and three places behind Chelsea, who lie seventh.