Trump raced into a 2-0 lead against Tom Ford and went into a 3-1 lead at the interval.
However he was pegged back by the world number 26 after the break as he got it back to 4-3 but Trump moved to within one of victory thanks to a fortunate kiss on a long red.
'Oh you lucky boy!' - Trump enjoys slice of luck against Ford
World champion Trump wrapped up victory with a three frame advantage as he looks to win his first ranking tournament as the new number one.
On the other table Selby also went into a 3-1 lead against Gary Wilson at the interval and like Trump he also benefited from a major slice of luck on a long red as he went 4-2 ahead.
However Wilson dug in and he eventually forced a decider against Selby thanks a break of 126.
An outrageous kiss on the pink after potting the blue set Selby up beautifully in the final frame and a break of 83 gave him victory.
Kiss benefits Selby in deciding frame
In the later quarter-finals. Mark Allen beat Ding Junhui 6-3 while Shaun Murphy downed Graeme Dott 6-4.