Sun won 6-2 5-7 6-2 in two hours 45 minutes.
In her post-match interview, the Te Anau-born Sun was in tears before composing herself with the help of a generous ovation from the British fans, the BBC reported.
"I don't really have the words right now."
The Kiwi qualifier went on to say her superb grass-court game had been aided by watching YouTube videos of past greats Roger Federer, Steffi Graf and Martina Navratilova from back in the day.
"It was just so amazing to watch them. Of course I couldn't watch them live but I was taking it it all on from the pros, and trying to do that for my game," Sun said.
Her sister and her mum were also in tears in the player box at Wimbledon.
Early in the third set Raducanu slipped on the grass and had a brief time out.
Sun broke the Briton twice in the third set and looked in control throughout.
Former world No 1 Ash Barty, who is now a BBC commentator, said Sun's performance showed her intent, bravery and courage.
Sun is the first New Zealand woman to make the fourth round since Dame Ruia Morrison in 1959.
Sun had announced her arrival at the UK's Grand Slam tournament by ousting world number eight Qinwen Zheng in the first round before beating fellow qualifier Yuliia Starodubtseva of Ukraine.
