The eight-year-old Doyen mare looked to have plenty on her plate when detached from the front three horses racing into the dip over a quarter of a mile from home.
She freewheeled down the hill, though, and cut into the deficit to get on the tails of the leaders at the second-last.
She was ridden to stay on into the lead coming to the last and bounded clear to win by nine and a half lengths at 15/2 from 10/1 on this step up in trip. Hollymount the 5/4 favourite, had no answers in second but was a length and a quarter in front of Raven Rule (5/1).
Trainer Jimmy Barcoe said: "The couple of runs over fences have stood to her, she jumped well and did everything brilliant today. Her run in Killarney was good, she wasn't far behind The Little Yank and that would be solid form. She ran well the last day too.
"We were always hopeful that she might win when stepped up in trip. I'd say she would get three miles on ground like that today and ridden that way too.
"The plan was to jump around, get her into a rhythm and take it from there. She was given a very good ride.
"It's hard to know what to do with her now. She has a mark of 106 over fences and you'd be hoping she'd be progressive. She could go to Listowel, we will just see what is on the programme. It would be good to give her a crack at something nice over a distance."
Influential Lady had won three times over hurdles and this was her first chase success.