Ebdon came storming back after losing the opening two frames, producing some outstanding snooker to win six in a row.
Fu made a good start in a tense opening frame, taking advantage of a double kiss on a red by Ebdon to clean up.
A slow start to the second saw Ebdon make another mistake as he blocked himself from the red he needed, and Fu took full advantage to move 2-0 up.
He was looking good in the third but missed the brown that should have seen him go on to win, and Ebdon stormed back with a break of 27 to snatch it.
Ebdon then scrapped his way back into the game, winning a tough safety exchange to take his first lead, 3-2, after the fifth.
After the break Ebdon looked like a different player, free in his rhythm as he piled up substantial breaks and left Fu sitting in his corner. He was cruising towards a century in the decisive eighth frame before missing a pink, but he had already done enough to go through.
Earlier, Mark Selby breezed through to the second round with a 6-1 rout of China's Ding Junhui.
He now faces John Higgins or Mark Allen in the quarter-finals.