O'Sullivan, 42, hasn't played competitively since he was knocked out of the World Championships by Ali Carter in April.
After Robertson missed a long red O'Sullivan came to the table and cleaned up on his very first visit with a break of 97.
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At times Robertson looked in fine form, knocking in a ton, but at others he looked lacklustre, missing some basic pots.
O'Sullivan was not without his faults but he rarely had to get out of top gear on his way to victory.
Although that didn't mean he didn't turn on the style for the crowd.
He will face Stuart Bingham in the next round.
Earlier on Wednesday world champion Mark Williams played some sensational shots on his way to a 6-3 victory over Anthony McGill in the second round of the Shanghai Masters.
Williams, 43, has looked in good form already this season, winning the World Open, and he took the opening frame.
McGill responded with a century break but Williams kicked up a gear to take the next two frames to go into the interval ahead.
He opened up the second session with a ton of his own and although McGill got another century on the board, he was powerless to stop the Welshman from progressing to the next round.
In the last eight Williams will face Barry Hawkins.
In Wednesday's other early match, Ryan Day beat John Higgins 6-5 in a thrilling match.
Welshman Day opened up with a break of 95 in the second to take a 2-0 lead before Higgins responded to get himself on the board.
The four-time world champion managed to level the match at 3-3 before the pair exchanged frames until 5-5, with Higgins taking the match to a decider thanks to a brilliant century break of 136.
Higgins makes remarkable three-ball plant
However, he could not get over the line as Day secured progression to the quarter-finals with a break of 87.
Day will face Kyren Wilson in the quarter-finals.
Shanghai Masters Round Two Results
- Ronnie O'Sullivan 6-3 Neil Robertson (Wednesday 1pm)
- Shaun Murphy w/o Stuart Bingham
- Judd Trump 2-6 Kyren Wilson (Tuesday 1.30pm)
- John Higgins 5-6 Ryan Day or Chang Bingyu (Wednesday 7am)
- Mark Selby 6-5 Zhou Yuelong (Tuesday 7:30am)
- Ding Junhui 6-3 Mark Allen (Tuesday 1.30pm)
- Barry Hawkins 6-3 Stephen Maguire (Tuesday 7.30am)
- Mark Williams 6-3 Anthony McGill or Yan Bingtao
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