O'Sullivan edged into the lead twice in the morning, but two magnificent century breaks levelled things up for Robertson, who finished the session 5-4 up.
However, he found himself facing even bigger problems when his cue-tip disintegrated in the sixth frame - but played on regardless.
'That's hurtful!' - Robertson takes lump out of cue tip
O'Sullivan lifts Shanghai title for third successive year
O'Sullivan was resurgent in the evening, though, rolling through four frames in succession to give himself a 9-5 advantage.
The Australian stayed in touch but O'Sullivan was not to be denied, wrapping it up 10-6 to secure his place in the final against Shaun Murphy on Sunday.
O'Sullivan downs Robertson to reach final
O’Sullivan wins third consecutive Shanghai Masters
O'Sullivan knocks in second ton against Murphy