It was the first time Ebdon had reached the last 16 of a ranking event since February, with the 45-year-old set to meet David Grace next.
The world number 34 was always ahead in the contest, keeping Bingham at bay before wrapping up victory with a 109 break in the ninth frame.
“Last night it looked like I was going home as I was 5-4 down against Dominic Dale,” said Ebdon. “I made two very good breaks to win 6-5 but I didn’t get to sleep until 3am and only had five hours sleep. This morning I ate five bananas, some apples and grapes and I felt fresh as a daisy.
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“I played an attacking game today, went for my shots and it’s a great win for me to beat someone of Stuart’s class. It’s nice to know my heart is still ticking.
“The table fitters here have taken a lot of stick in recent days but they did a magnificent job last night and the conditions were very good today.”
Elsewhere, John Higgins won 6-2 against Ali Carter, who suffered from abdominal pain during the match. Higgins will meet friend Jamie Burnett in the next round.
“It’s a very good win for me,” said Higgins. “I was delighted to be 3-1 up at the interval because I could have been 3-1 down, and I knew Ali would have been gutted. I am back competing which is a good feeling. I know I can turn up to tournaments and have a chance to win.
“Jamie has been playing well. I prefer not to play the other Scots, it won’t be easy. we used to practise together but I don’t think he has played anyone in practice for about the last five years, he only does an hour or two on his own here and there.”
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