The Rocket took the opening frame with a break of 90 before Trump hit back with a 53 in the second.
The world number three looked on course to take the third following a break 52, but a careless safety allowed Sullivan to return to the table, pot a long plant, and bag a break of 83.
The six-time world champion was in fine form and produced a clearance of 99 to take a 3-1 lead heading into the mid-session interval.
O'Sullivan needed three visits in the sixth frame before a 62 break made it 4-2 and although Trump won the next to reduce his deficit, a fully focused O'Sullivan produced a total clearance of 127 and a run of 52 to seal the win.
The standard of play was nowhere near as high on the other table as Ricky Walden made his top break of 74 in the final frame of a 6-2 win over Mark Allen, whose best contribution was a 69 in frame two.
Earlier in the day, Barry Hawkins beat top seed Zhao Xintong 6-3 to set up a quarter-final with Yan Bingtao, who defeated David Gilbert 6-4.
Hawkins, who finished just £1,500 ahead of Mark Selby to claim the final qualifying place for the event, made breaks of 63, 91, 94, 71 and 50 against UK Championship winner Zhao.
Yan showed no signs of a hangover following his 9-0 whitewash at the hands of Zhao in the German Masters final as he made breaks of 100, 80, 66, 135 and 123.
Gilbert rallied to take the next three frames in succession but Yan held his nerve to seal victory with a break of 59.