The defending champions raced into a 29-0 lead with tries from Lote Raikabula, Victor Vito (2), captain DJ Forbes and James Kamana before Neumi Nanuku scored Fiji's only try of the match.
Fiji, just as in the Dubai final last weekend, had two players sin-binned in a match which New Zealand controlled from start to finish with Israel Dagg completing the scoring with his first touch after coming on as a replacement.
The title is New Zealand's fourth consecutive in the IRB Sevens World Series after their victories in London, Edinburgh and Dubai and gives them a maximum 40 points from the opening two tournaments, eight more Fiji.
South Africa, semi-finalists in both Dubai and George, are third with 24 points, four more than Argentina, who followed up their Plate victory in Dubai with a Cup semi-final in George. England and Kenya are next, both with 12 points.
A hat-trick from Zar Lawrence had helped New Zealand beat Argentina 38-14 in the semi-final, the IRB Sevens World Series champions having beaten a committed USA 36-0 in the quarter-final.
Fiji's manner of victory in their semi-final was nowhere near as comfortable, the islanders scoring tries from Akuila Nawerecagi and Tomasi Mawa in the last two minutes to silence the vociferous home support with a 21-12 victory over South Africa.
The Springbok Sevens paid the price for not converting their attacking opportunities into points and experienced the same disappointment Scotland had endured at their hands in the quarter-finals when Vuyo Zangqa scored in the dying seconds to snatch a 21-17 win.
Neumi Nanuku had earlier scored two of Fiji's tries in their 24-12 defeat of Kenya, the Africans losing in the last eight of the Cup for the second tournament in a row. Argentina meanwhile had to come from behind twice to beat Samoa 22-19 in the other quarter-final.
