Chasing a record eighth world title in the modern era, O'Sullivan made a steady start in a scrappy opening frame before Si, one of the sport’s most exciting young talents, fired back with a superb century.
But the 22-year-old from China was soon undone by a string of missed chances, allowing the sport's most decorated player to pull away.
O'Sullivan punished the errors ruthlessly, compiling three half-century breaks to go 4-1 in front.
The Rocket eventually closed the session in style with a vintage 121 break, underlining his dominance.
Elsewhere in Tuesday afternoon’s session, world number one Judd Trump delivered another impressive display of break-building to move 5-3 ahead of Luca Brecel.
Trump rattled in his 101st and 102nd centuries of the season, putting him within touching distance of Neil Robertson’s single-season record of 103, set back in 2013/14.
The 2019 champion raced into a 5-1 lead with clinical scoring, but Brecel, who claimed the world title in 2023, showed his fighting spirit with breaks of 68 and a sparkling 128 to reduce the deficit and keep the match finely balanced heading into Wednesday morning's continuation at 10:00 BST.
Meanwhile, in another tantalising all-time-greats showdown, John Higgins holds a 5-3 advantage over Mark Williams after their first session.
This marks their first Crucible meeting since the 2018 final, when Williams edged out the Scot in a classic encounter.