Businessman Goldsmith, estimated to be worth £30million, is the younger brother of the Duchess's mother Carole Middleton and attended the weddings of both Kate and Pippa.
Prosecutor Kate Shilton told the court Mrs Goldsmith fell down after her husband threw what was described by their taxi driver, Daniel Shepherd, as a "left hook".
Goldsmith pleaded guilty to one count of assault by beating.
"She was asking about what Jacob liked and he said he liked aeroplanes and was asking if he'd seen a Spitfire and we said we liked going to the Science Museum and RAF museum".
"Mrs. Goldsmith said she couldn't recall how it happened but her husband punched her in the face with a closed fist to the left side of her face", said Shilton.
Stepping out for the solo royal engagement on the wet and cold day, Kate Middleton opted for knee-high black boots with a slight block heel, which she appeared to wear over black leggings.
Kansas basketball: Devonte Graham will shine in Champions Classic
I didn't realize how good ( Vermont ) was until I watched the tape. "I mean, they're who they always are". For proof of this assertion, we only need to look at Calipari's previous slowest starting team, 2009-10.
After falling to the floor, she remained flat-out with her eyes closed for around 15 seconds before waking up and staggering to her feet, the prosecutor added. During this time, the uncle of Kate Middleton seemed "panicked" and was " back-and-forth in the house trying to make it fit ".
The court heard the couple began to argue while in a taxi after a charity event, then continued the argument on the street outside their home.
At the police station, Goldsmith told officers he had pushed his wife hard with his left hand, but denied using a hook.
Kate Middleton's uncle Gary Goldsmith appeared in court Tuesday, and admitted to physically assaulting his wife following a drunken night out, according to the BBC.
Ahead of sentencing, which will take place on 21 November, chief magistrate Emma Arbuthnot said she was "excluding custody and looking at a community order". Speaking after meeting Kate, Billy said: "She was saying William was sort of similar and I just wanted to let her know how Family Action have been there for me and I think they need more support". Their mother worked in a shop and also did accounts, while their father was a painter and decorator.