The Irishman scored the biggest win of his career - the first in a Grand Tour - by beating Elia Viviani (Quick Step Floors) and Niccolo Bonifazio (Bahrain-Merida) after 159km of relatively flat racing on the Italian coast. The stage was a 159-km run from Pizzo Calabro near Vibo Valentia to Praia a Mare near Cosenza.
By that stage Colombian Chaves had broken clear and looked to have the stage win sealed.
"I feel relieved", Bennett, who was second, third, third and third on stages last year and third twice in this year, said afterwards.
"They were really far back and I thought there was no way we'd come back because there was the chicane still to come and I thought for sure it would be one line so even if we did get back, would I still have the power still to go?"
BC-CYC-Giro d'Italia, 2nd Ld-Writethru, 384 Bennett wins 7th stage as Yates maintains Giro d'Italia leadAP Photo PRA102, PRA101, PRA105, PRA106Eds: Updates with Yates quotes.
"I'm obviously delighted to get my first Grand Tour victory".
New Zealand's George Bennett finished towards the rear of the peloton in 30th and remains ninth overall.
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Given the high stakes of their meeting , one might expect a tenser, less inviting image. We looked them straight in the eye and they said to us verbatim, 'God bless America.
Yates is one of the favourites for final victory, along with reigning champ Tom Dumoulin of the Netherlands and Briton Chris Froome.
Froome is now eighth in the generation classification, one minute and 10 seconds behind Yates.
"I felt really good", Yates said.
The result had no impact on the top of the general classification with Simon Yates of Mitchelton Scott finishing safely and retaining the Maglia Rosa head of stage 8. "The guys then did an awesome job just to keep the break within three minutes, and finally we got some help from other teams".
"Tomorrow, if I have the legs, I might try something".
Saturday's eighth stage is a 208km ride from Praia a Mare to Montevergine di Mercogliano.
In fact, many of them are packed with mountainous climbs and it will be a struggle for some of the fast man to make it as far as Rome on 27 May.