O’Sullivan lost to Stuart Bingham 13–10, and Jak Jones defeated world number two Trump 13–9.
On the other side of the draw, David Gilbert defeated Stephen Maguire 13–8 to get to the semi-finals.
He will now go on to beat fellow Englishman Kyren Wilson, who defeated four-time Scottish champion John Higgins 13-8.
Before the competition, Trump and O’Sullivan were picked as the favorites to win at the Crucible Theatre.
Additionally, the draw had opened up the possibility of a tantalizing final-four match between the two, with O’Sullivan pursuing a record-tying eighth world title in the modern era after drawing level.
However, “The Rocket’s” luck ran out when he was unable to overcome Bingham, the 2015 winner, who maintained his composure and hit an incredible break of 104 to win three straight frames.