Trump compiled four half-century breaks in his 6-4 win over Scott Donaldson 6-4 in Daqing.
The world champion will usurp O'Sullivan if he secures a second International Championship title.
Trump downs Donaldson in China
Meanwhile, Mark Allen continued his title defence with a 6-1 victory over Mark Davis in his second round tie.
The Northern Irishman beat Neil Robertson in last year's final, and he enjoyed a top break of 101 to set up a clash with Ali Carter in the last 16.
Shaun Murphy overcame Yan Bingtao while Graeme Dott also won 6-3 against Stuart Bingham, with sixth seed Mark Selby recovered from a two-frame deficit to beat Ben Woollaston by the same scoreline.
John Higgins is safely through to the last 16 after he produced a 71 clearance to end Elliot Slessor's hopes. Slessor dished out the highest break with a 110 closing the gap to 5-2, but Higgins took the next frame to seal the win.
Round Two results
Liang Wenbo 6-4 Daniel Wells
John Higgins 6-3 Elliot Slessor
Neil Robertson 6-5 Ricky Walden
Gary Wilson 6-2 Luca Brecel
Mark Selby 6-3 Ben Woollaston
Tom Ford 6-5 Kyren Wilson
Andrew Higginson 6-4 Jimmy Robertson
Jak Jones 6-3 Robert Milkins
Ding Junhui 6-1 Xiao Guodong
Graeme Dott 6-3 Stuart Bingham
Judd Trump 6-4 Scott Donaldson
Shaun Murphy 6-4 Yan Bingtao
Allister Carter 6-3 Kurt Maflin
David Gilbert 6-1 Anthony McGill
Joe Perry 6-2 Stephen Maguire
Mark Allen 6-1 Mark Davis
Selby recovers from two-frame deficit to beat Woollaston