O’Donnell, who regained his tour card for this season, recovered from dropping the opening frame to frustrate the reigning world champion and complete a 4-2 victory to set up a fourth-round clash with either Ding Junhui or Tom Ford.
“It felt like I played really solid out there today,” O’Donnell told Eurosport. “It felt like I didn’t really miss too many and I scored quite well.
“I put him under pressure when I got my chances and thankfully got through it.”
O’Donnell had won the only previous two meetings between the pair but fell behind early. Brecel, who survived a scare to beat James Cahill in the last round, needed a couple of chances but a break of 57 got him over the line for a 1-0 lead.
The Belgian then had a chance to double his advantage in the next and could perhaps count himself unlucky when an attempt to split the pack from the blue went wrong when he was on 29.
O’Donnell got to 23 in response before missing a tricky red but returned to knock in 59 and level at 1-1.
Brecel appeared increasingly aggravated by the pace of his opponent’s play and was frozen out in the third as O’Donnell moved ahead with a break of 75, and threatened to combust in the fourth frame when he missed a tricky pink after another unfortunate pack split.
To his credit, O’Donnell stuck to his task and moved within one of an upset victory at 3-1 with another composed 50-plus break.
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Watch as O’Donnell closes out surprise victory over world champion Brecel
Another split went wrong for Brecel when he had a 27-point lead in the fifth frame, but he eventually clinched it after a marathon safety battle to halve his deficit, before O’Donnell sealed a deserved victory.
Again the break-off shot from the Belgian was poor and a break of 82 booked O’Donnell’s place in the fourth round.
Matthew Selt recovered from 3-1 down to beat Mark Selby and book his place in the fourth round.
Both players had chances in every frame, but it was the four-time world champion who uncharacteristically faltered with the winning line in sight.
They shared the opening two frames before Selt was made to pay for missed opportunities in the third and fourth as Selby pounced with breaks of 67 and 50 to move 3-1 clear.
But Selt set up a deciding frame and prevailed after Selby missed a simple brown.
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Watch as Selt clinches big upset over Selby at Scottish Open
There was another upset as Noppon Saengkham beat Ali Carter 4-2.
The Thai player lost the first frame but responded with a century before moving 3-1 ahead.
Carter responded with a total clearance of 138 but was eliminated when Saengkham knocked in a 79 in the sixth frame to progress.
Elsewhere, breaks of 53, 100 and 56 helped Anthony McGill recover from 1-0 and 2-1 behind to beat Pang Junxu 4-2.
The Scotsman kept his hopes of lifting his home title alive with a battling performance and will meet Liam Graham or Sanderson Lam next.
John Higgins made sure of a spot in the quarter-finals following a tricky 4-3 victory against Ricky Walden that crept into the early hours of Thursday morning.
It was Walden who got off the mark first with a break of 75 to move ahead in the race to four.
Higgins hit back with a superior effort of 81 to draw level, but a tightly fought third frame went to the Englishman, 67-61.
Subsequent 50+ breaks from the home favourite put him firmly in control of the match and within a frame of victory.
