He had jumped out to move a herd of heifers which had closed in around his tractor, accidentally knocking it back into gear as he did so.
The tractor ran him over before crashing into a gate.
Last night his family were optimistic, saying he was smiling and the surgery appeared to have gone well.
"We're happy with the way things have gone today," said his daughter Sharon Laurenson. "It's early days but he's eating and coherent and back to his normal cheeky self."
She added: "His name's Speedy so we're hoping for that - a speedy recovery." Mr Speedy's son Mike was also upbeat about how the surgery had gone.
"I speculate it's gone as well as can be expected, and maybe even a little bit better, so that's really cool," he said.
Mr Speedy was well known in the area, and Mike said he had been inundated with calls from well-wishers.
"It's unbelievable how many telephone calls I've had today," he said. "I could go to the beach and let everybody on the Hauraki Plains run the farm.
"Everybody's been offering help, the kind of support you get in a real community."
And the 81-year-old hasn't been letting his stint in hospital get in the way of running his farm or enjoying himself, giving his son a list of jobs to do and "chatting up the nurses".
Mike described his father as "unbelievably lucky".
"You can't run over too many 81-year-olds and get away with it," he said. "He's got the blood pressure of a 40-year-old, and he still hunts and fishes and all that sort of drama. He's a bit of a hard case."
Chris Deacon, an intensive care paramedic with the Westpac rescue helicopter, said Mr Speedy was a "tough old coot".
