The Aussie survived a barrage of five century breaks from the Rocket to win the final-frame decider and book his spot in the showpiece.
O'Sullivan looked near unstoppable in the early exchanges as he took a 4-1 lead. However, Robertson battled back valiantly and went 8-6 up himself.
The Rocket found his second wind and was able to move within one frame of the final after moving 9-8 ahead.
Despite his advantage, it was Robertson who showed cold blood as he raced to victory.
Speaking to World Snooker, the 40-year-old said: "It's a huge win. I thought it was a brilliant match. You won't see better quality from two players than the first session today.
"He made some unbelievable breaks tonight out of absolutely nothing. Most players would dream of making 30 in those situations and he was making centuries. You have to enjoy it while you are in the chair but also not accept that you are going to lose.
"You always have to enjoy playing the greats of the game because you never know how long it is going to happen for. Whenever I play the likes of John Higgins, Ronnie or Mark Williams I always savour the moment. These guys were idols of mine growing up. I never thought I would meet them let alone play them."
Despite being on the end of a defeat, O'Sullivan also made history as he became the first player to make five centuries in two consecutive matches.
The Rocket produced five three-figure scores against Mark Williams in a similarly dramatic 10-9 victory in the earlier round.
The six-time world champion has now faced Robertson in four high profile games this season, losing three of them. The other two defeats came at the Cazoo Masters and the Cazoo Players Championship.
O'Sullivan's only win over the Aussie this season came in the final of the Cazoo World Grand Prix back in December.
Robertson will now look ahead to Sunday's final, where he will take on either John Higgins or Luca Brecel in a best-of-19 frames match.