The Fury's speed advantage was underlined by Guy Privett's effort to make it 2-0, but it was Erik Aceituno's volley from outside the box that illustrated the difference in class.
The left-footer controlled a cross before burying the bouncing ball off his laces, making it 3-0 early much to the joy of Fury manager Dave Cook.
Worse was to come for the visitors, who went 4-0 down into the break due to Garnham springing himself free on halfway before drilling home a finish off his left.
The match failed to reach the same heights in the second half, leaving former Tauranga City player Connor Irvine to supply a rare highlight by forgetting momentarily which team to encourage.
Matt Collins pulled back a goal with a header that Fury disputed crossed the line, but that was cancelled out by a goal to impressive, if individualistic, striker Federico Gomez.
The result, along with Tauranga City United's win in the Chatham Cup, raises the question as to what would happen if the two sides ever got the chance to meet.
Cook was enthusiastic about his team's chances of promotion after the match, but knows with the crosstown rivals' top team also looking headed for promotion, he may have to mount another campaign to get his match.
AFC Fury 5 (Lee Garnham 2, Guy Privett, Erik Aceituno, Federico Gomez) Tauranga City United 1 (Matt Collins)