The five-time world champion avenged last year's quarter-final defeat to reach Sunday's final.
Trump took the first two frames but a break of 143 in the fourth helped O'Sullivan level before he moved ahead.
The defending champion made it 3-3 thanks to a break of 109 as the next two frames were shared and then went 5-4 up with a run of 123.
The Rocket hit back to take the tenth frame before keeping his cool to claim the decider after Trump had fluffed a golden opportunity when in the balls.
O'Sullivan will face either Shaun Murphy or Mark Williams in the final with the pair due to play on Saturday.
The Rocket told www.worldsnooker.com: “It was a good match. I felt a bit sorry for Judd because I know how hard he works. He had a good chance in the last frame. It’s tough on him but he’s a strong character and he’ll come back from it. You have to take the rough with the smooth in sport.
"I'll go out there in the final and try to be as quick as I can, win or lose. I’ll try to keep it free flowing. I’m not the most confident player – I never fancy my chances until I hit my first ball. The build up is always the worst part for me.
"I’ve had fantastic support this week from a great crowd. It has been very noticeable that the crowd have really got behind me – I’m so pleased to have given them something to cheer about. This has been a quality event with quality players."
The 42-year-old is aiming for his fifth ranking title of the campaign, having already won the English Open, Shanghai Masters, UK Championship and Ladbrokes World Grand Prix. He has also won 32 of his previous 46 ranking finals.
Victory on Sunday would see him equal the record of five ranking titles in a single season, held by Stephen Hendry, Ding Junhui and Mark Selby. The £125,000 top prize would also push his prize money for 2017/18 close to £800,000.
Sky Bet make O'Sullivan the odds-on favourite at 1/3 to win the tournament.
Murphy set up his showdown with Williams in the last four after he beat Anthony McGill 6-5 in the quarter final on Friday.
"I’m absolutely delighted,” said Murphy in quotes on worldsnooker.com.
“Before coming here I hadn’t played at all since the Welsh Open. Today’s match was a bit scrappy here and there but it was tough match play snooker and I am thrilled to win.
“I am in trouble (with the injury), I have got problems. I have had some great physio a few times this week from a local guy called Barry Craven – without his treatment I may have had to pull out. He has worked some magic but I am by no means healed. It is painful but I felt I’d had enough time off and I wasn’t going to miss this event.
"I’ll have a hot bath tonight and avoid going out for any triathlon training! Then tomorrow morning I’ll see whether I need more physio."
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