Walsh enjoyed an armchair ride for much of the three-mile race, sitting still on the seven-year-old until after the final fence when the 5-6 favorite bounded up the hill to win by 3 1/4 lengths.
Time For Rupert (16-1) was second and Powerstation (33-1) third.
"He's a horse that wouldn't want to be in front too long. He has a terrific engine and it was a good round of jumping," Walsh told Channel Four television.
Victory made up for disappointment for Nicholls, the leading trainer at the festival for the last four years, on Wednesday when heavy favorite Master Minded was well beaten in the Queen Mother Champion Chase.
"I can sleep a lot better now after Big Buck's won," said Nicholls, who saddles hot favorite Kauto Star and second favorite Denman in the Cheltenham Gold Cup on Friday, the final day of the festival.
"He worked very moderately on Saturday - but that's just his character. He's a bit quirky, a bit of a boy. You don't mind training those sort of horses but they give you a few sleepless nights because you start having doubts.
"You have to get into his head a little bit but there is something very very special about him. I felt today there might be a few things against him but I don't know why I was worrying - he never hit a flat spot." Big Buck's' victory was greeted by loud cheers by race goers as light rain fell on the Gloucestershire course. Defeats suffered by Irish hotpot Dunguib on Tuesday and Master Minded on Wednesday, two of the festival "bankers" for many, had left punters out of pocket.
