The seven-time world champion was beaten 13-10 by his compatriot at the Crucible in Sheffield.
'The Rocket' was up against it from the start, conceding three of the first four frames to Bingham.
A battling performance followed as O'Sullivan clawed back to take a 8-6 lead, before the Englishmen were tied at 10-10.
Bingham, who became visibly emotional, then claimed the next three frames to beat the world number one.
Speaking afterward, O'Sullivan told BBC Four: "That's just the way it goes. I'm actually really happy, to be honest with you, I feel like I'm actually getting through the ball, which is more important for me at this stage. It's been a bit of a worrying couple of years.
"So, for me, not the win that I'd have liked to have had, but that's just snooker, that's the way it goes.
"Good luck to Stuart, he played a fantastic match and deserved his victory.
"I'm just pleased that I competed and that I was cueing okay. Just a few errors here and there, but on the whole, not too bad."
On being knocked out alongside Judd Trump, he added: "You get a lot of people talking, but I was just coming here knowing it was just going to be another difficult tournament - just like it is when you enter any tournament.
"No-one's got any divine right to win any match. A lot can happen in a game of snooker - that's just sport."
Shortly after his sensational victory, Bingham said: "I've had a little cry at the back there. Unbelievable."
"I was just enjoying it out there."
On missing an easy pink into the middle pocket that gave O'Sullivan a chance to get back on the table, he admitted: "I had to have a laugh to myself. I'm like: 'All I've got to do is just roll this to the pocket'.
"I've just pulled it and it's gone near knuckle."
Bingham will face Jak Jones in tomorrow's semi-finals, following the Welshman's win over Trump.
