"It was quite a tricky fence, that narrow fence on an uphill slope, and I thought I would just give him a breather there," said 52-year-old Nicholson.
"But he felt pretty good. He's a horse that seems to like going back to certain places. He was squealing and shying and jumping extravagantly in the warm-up.
"To win here three times in a row on a horse that was born round here and is named after a local landmark feels pretty good. Bring on Burghley!"
Avebury, who is Nicholson's reserve horse for next month's Alltech FEI World Equestrian Games, is also a back-to-back Land Rover Burghley Horse Trial winner. Nicholson is keen to complete that hat-trick at the September event.
Sir Mark Todd and Leonidas II went into the final cross country phase in second place, but their 11.2 time penalties saw them slip to ninth.