Meech, who started the day in fifth, managed to hook into the extra pressure and his fourth place in the medal race was enough to propel him into the medals. Great Britain's Elliott Hansen had already wrapped up gold before the race and Australia's Matthew Wearn was second.
"It's fantastic," Meech said. "In the past when I haven't sailed well I have been at the back of the fleet. It's nice to have a bad week and still pick up a medal at the end of the week.
"But I think a lot of guys were like me and took a little bit of time off after the world championships so not many were really on form. But to come away with a medal, I'm pretty happy with that."
It rounds out a very successful past 12 months on the international circuit for Meech, who won his first World Cup title in Gamagori late last year and backed it up with silver medals at the Hyeres World Cup, Princess Sofia regatta in Palma and the Laser Europeans in La Rochelle. He also led for a few days at last month's world championships before having to settle for fourth.
His main target, however, is the 2020 Tokyo Olympics and one of the main aims of this regatta was trying to better understand the Olympic venue. But the 27-year-old admits he was left scratching his head at times this week given the predominance of tricky offshore winds and feels he's still some way from getting a handle on the venue.
"It hasn't really felt like that this week," he said. "The training we had leading into the regatta was totally different to the conditions we had this week, with the wind coming from the other direction. It was some of the best sailing that I've ever done."
Meech will now return home for a break and to do some sailing in other boats but a number of New Zealanders will remain in Japan for another regatta, Enoshima Olympic Week, starting in a few days' time.
Results and standings after the final day of the World Cup regatta in Enoshima, Japan, today:
Laser (59 boats)
1st: Elliot Hanson (GBR) 11 6 14 1 3 6 (17) 5 1 12 - 59 points
2nd: Matthew Wearn (AUS) 3 12 25 4 19 5 6 19 (27) 4 - 97 pts
3rd: Sam Meech (NZL) 4 (35) 17 2 6 19 7 18 25 8 - 106 pts
6th: Tom Saunders (NZL) 15 18 8 3 8 22 1 15 (28) 20 - 110pts
18th: George Gautrey (NZL) 5 36 11 (60 BFD) 16 9 42 10 32 - 161 pts
Laser Radial (53 boats)
1st: Marit Bouwmeester (NED) 2 (23) 4 5 9 6 2 2 - 30 pts
2nd: Josefin Olsson (SWE) 15 1 10 2 17 2 (28) 4 - 51 pts
3rd: Emma Plasschaert (BEL) 5 3 14 (15) 8 5 14 8 - 57 pts
31st: Olivia Christie (NZL) 25 4 21 (45) 44 35 31 - 160 pts
Nacra 17 (25 boats)
1st: Jason Waterhouse / Lisa Darmanin (AUS) 6 5 3 5 3 2 (8) 1 7 2 - 34 pts
2nd: Ruggero Tita / Caterina Marianna Banti (ITA) 1 1 1 1 1 (12) 4 6 12 9 - 35 pts
3rd: Vittorio Bissaro / Maelle Frascari (ITA) (11) 2 2 2 7 3 9 5 8 4 - 42pts
6th: Gemma Jones / Jason Saunders (NZL) 2 3 10 3 (26 DSQ) 10 12 3 5 20 - 68 pts
Finn (21 boats)
1st: Nicholas Heiner (NED) 5.4 DPI 6.4 DPI 1 (8) 4 4 3 7 2 - 32.8 pts
2nd: Giles Scott (GBR) 6 1 2 6 (10) 2 9 5 5 - 36 pts
3rd: Edward Wright (GBR) 7 3 4 (9) 3 6 4 2 8 - 37 pts
5th: Andy Maloney (NZL) (14) 8 12 7 9 1 5 1 6 - 49 pts
6th: Josh Junior (NZL) 2 6 8 3 6 10 7 12 (18) - 54 pts
49er (27 boats)
1st: James Peters / Fynn Sterritt (GBR) 4 3 5 1 7 8 (17) 9 15 2 - 54 pts
2nd: Logan Dunning Beck / Oscar Gunn (NZL) 3 5 8 6 9 17 5 (22) 3 16 - 72 pts
3rd: Lukasz Przybytek / Pawel Kolodzinski (POL) 2 8 3 17 5 (23) 4 5 8 20 - 72 pts
13th: Josh Porebski / Trent Rippey (NZL) 19 22 2 10 13 5 9 (25) 14 - 94 pts
18th: Isaac McHardie / William McKenzie (NZL) 21 6 20 14 (24) 9 10 8 13 - 101 pts
49erFX (24 boats)
1st: Martine Soffiatti Grael / Kahena Kunze (BRA) 1 5 2 1 1 (13) 1 8 - 19 pts
2nd: Alex Maloney / Molly Meech (NZL) 19 3 1 2 4 12 (24) 4 - 45 pts
3rd: Klara Wester / Rebecca Netzletr (SWE) 5 (25 UFD) 12 6 8 8 3 6 - 48 pts
Men's 470 (32 boats)
1st: Keiju Okada / Jumpei Hokazono (JPN) 5 2 1 2 12 2 (16) 8 - 32 pts
2nd: Mathew Belcher / William Ryan (AUS) 3 (15) 5 1 11 5 5 10 - 40 pts
3rd: Daichi Takayama / Kimihiko Imamura (JPN) 7 9 6 5 2 (13) 10 4 - 43 pts
28th: Paul Snow-Hansen / Daniel Willcox (NZL) 19 32 14 18 26 19 (33 RET) 14 - 142 pts
Women's 470 (23 boats)
1st: Afrodite Kyranakou / Anneloes van Veen (NED) 2 5 6 2 6 (8) 3 5 - 29 pts
2nd: Ai Kondo Yoshida / Miho Yoshioka (JPN) 11 1 2 11 (12) 4 2 2 - 33 pts
3rd: Benedetta di Salle / Alessandra Dubbini (ITA) 5 2 7 (13) 5 2 10 3 - 34 pts
22nd: Courtney Reynolds-Smith / Brianna Reynolds-Smith (NZL) 21 20 20 (23) 19 20 - 141 pts
Men's RS:X (40 boards)
1st: Kiran Badloe (NED) 3 2 8 2 4 11 (17) 4 4 - 37 pts
2nd: Mateo Sanz Lanz (SUI) 9 (20) 12 1 7 4 1 9 8 - 51 pts
3rd: Pierre le Coq (FRA) 10 3 4 3 9 (41 UFD) 8 7 10 - 54 pts
Women's RS:X (30 boards)
1st: Peina Chen (CHN) 1 3 10 3 8 4 1 (13) 4 - 34 pts
2nd: Lilian de Geus (NED) (21) 1 1 10 15 1 8 3 6 - 45 pts
3rd: Yunxiu Lu (CHN) 2 5 4 (17) 1 2 17 14 2 - 47 pts