The 23-year-old New Zealander put in a time of 44.638.
The silver medal went to the Ukrainian Inna Osypenko-Radomska, while Hungarian Natasa Douchev-Janics took bronze. Both women were winning their second medals of the Games.
In the last Canoe Sprint race of the day and the Games - the men's K2 - Russia's Yury Postrigay and Alexander Dyachenko took gold.
Belarus came in second and Great Britain's Liam Heath and Jon Schofield third.
Carrington, who wears a greenstone Maori necklace when racing for 'wildtail strength and protection', said: 'You can only dream of being an Olympian champion.
'I have been working for this for the last year and it has been on my mind, preparing for it.
'You can never predict how fast everyone is going so I just went as fast as I could.
'For me to do my best, you need to enjoy what you're doing. I do love what I am doing. Everything is just awesome.'