A video captured by the family shows the bounce house flying high into the air.
"Is everyone accounted for?" a woman's voice asks in the video as the bounce house soars overhead.
The bounce house can then be seen flying toward some power lines and a transmission tower.
"It's going to hit the power lines!" a man's voice says.
The man proves correct, and the bounce house strikes the power lines, setting off a flurry of sparks.
The National Grid said workers removed the bounce house Saturday. A spokesman said power was temporarily shut off to protect the workers.
Michael Gersitz, owner of Party in Buffalo Bounce House Rentals, said the bounce house likely was not adequately anchored.
"I'm willing to bet that it wasn't properly secured just because I've done thousands of rentals and I have never had one problem. Either that or some sort of crazy wind gust, but I highly doubt that, most of the time when they're properly secured there's no problem and you know it's a fun amusement device for kids," Gersitz told WIVB-TV.