Going into the evening session 9-7 in front, Robertson reduced his arrears to one as he built a score of 68 over two visits to the table before missing a red. With a deficit of 52 points to make up, O'Sullivan decided to concede the frame.
'The Rocket' was clearly in no mood for safety play and quickly notched a break of 104 to stretch his lead again to two frames.
Robertson looked to respond in the next frame but missed the black off its spot when seemingly well set on 44. The mistake was punished by O'Sullivan who knocked in a break of 77 and then followed up with an effort of 100 in five and half minutes to go into the mid-session interval 12-8 ahead.
O'Sullivan looked set to wrap up the match quickly after the break and looked in a great position to do so but missed the black ball off its spot after he had potted a stunning long red.
It would be the last ball which O'Sullivan would pot in the next two frames as Robertson began to mount his comeback with breaks of 89 and 77.
But it came to an end as O'Sullivan sealed victory in the 23rd frame of the match with a break of 59 to set up a date with Stevens in the semi-finals.
A six-frame streak put Ronnie O'Sullivan ahead in his World Championship quarter-final against Neil Robertson, coming from 5-3 down to lead 9-7.
'The Rocket' cut a somewhat petulant figure whilst falling behind to the Australian, but approached their second session full of focus and confidence as he powered to six frames in a row.
Robertson, whose limited chances to get to the table were disappointing, eventually found a little flow with the final pair of frames of the afternoon to keep the score competitive, but it is O’Sullivan who now holds the cushion of two heading into the climax of their contest from.
Frames nine and 10 of the last-eight battle between two of the remaining tournament favourites were almost over before they began: O’Sullivan was at his smoothest with runs of 44 and 54 in the former and 97 in the latter to level at 5-5.
A 62 break was the highlight of frame 11 as O’Sullivan re-took the lead, and the three-times former World champion soldiered his way to another to whitewash the pre-interval action and lead by two.
The action following the break was more back-and-forth, but the Englishman continued to have the edge with stronger visits and more confident long potting, casting doubt as to whether or not the 2010 Crucible kingpin could recover.
But a tense battle of wills in frame 15 saw Robertson prove his fighting spirit has not faded with a run of 29 to seal the most error-strewn frame of the match so far.
And a composed 63 break, which resembled O’Sullivan’s own style of play with the manner in which it accelerated from a measured opening, finally gave the 30-year-old some real building time.
More importantly, it prevented the contest from slipping from his reach; a 10-6 deficit against an in-form Rocket may well have been too big a task in the evening’s finale.
Neil Robertson snatched the final frame of the session to take an early 5-3 lead over Ronnie O'Sullivan in their World Championship quarter-final in Sheffield.
The two former Crucible winners appeared evenly matched in an unpredictable encounter which swayed from flowing break building to foul-strewn defensive play and saw each man make a century apiece at 100 precisely.
O'Sullivan's came in the second frame en route to taking a 2-1 lead, whilst the Australian completed an identical score to move ahead again at 3-2.
And after a lovely 93 from O'Sullivan levelled the contest once again after six frames, Robertson grafted his way to an advantage heading into tomorrow's second session despite 'The Rocket' appearing to have 4-4 wrapped up on the final colours.
Robertson required a third visit to the table in the first frame to finally get building, but when he did, his 59 and a foul from O’Sullivan during his comeback run of 24 drew first blood.
O'Sullivan turned the score around with his century following an initial 18 from the Australian as the 2008 champion gradually gained command of the table, before a half-ton (51) allowed him to clinch 2-1 on the colour trail.
Robertson's own half century at 58 combined with an early run of 30 to put frame four beyond reach, and nothing separated the two tournament favourites as the mid-session interval approached.
The pendulum once again swung the way of Robertson with a wonderfully meticulous 100 before O’Sullivan fired back immediately with his 95 for 3-3.
But the man who claimed his first world title two years ago produced a late flourish of five red-black combinations in the latter stages of the seventh before again making a late dash for the finish line in the final frame of the session to create daylight in the tie for the first time.