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Robertson went 3-0 up but O'Sullivan - who declared himself underwhelmed by his own performance - gained a vital foothold with a 114 break.
The world number 15 had been struggling with a neck injury following a car crash on Monday night, but was fit enough to take his place at Wembley on Tuesday.
Meanwhile, O'Sullivan, who plays Peter Ebdon in the quarter-final, suggested his current form was a shadow of that which has seen him lauded as the most talented player the sport has ever seen.
"I don't want to have to rely on the occasion of being 3-0 down in front of a big crowd to salvage some pride. I can't pot a ball in practice.
"I wasn't surprised to be 3-0 down," he told BBC Sport.
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Ronnie O'Sullivan won a high-quality match against Neil Robertson 6-4 to reach the last eight of the Masters.