Murphy capitalised on an error strewn performance from Bingham, who looked a shadow of the man who trounced Jamie Cope in the previous round to set up a semi final meeting with John Higgins with a comprehensive 5-1 victory.
But Trump was pushed all the way by a typically-resilient Dott, who came back from 4-1 down before losing 5-4.
Trump punished a simple missed red from Dott with a break of 73 to take the opener and came out on top at the fourth time of asking in an error strewn second frame after twice handing Dott a reprieve when in the balls.
Dott was again in first in frame 3 with a break of 32 and a further mistake from Trump was all the Scotsman needed to get on the scoreboard.
Both players had their chances to take the fourth but it was Trump who was the more composed when it mattered, knocking in a frame winning clearance to maintain his two frame cushion.
Dott had the first chance in the next but again failed to make the most of his opportunity and a break of 52 put Trump a frame away. An opening break of 40 put pressure on Trump in the next and Dott made sure of extending his visit for another frame at his next visit to the table.
The Dott revival continued in the next, the pint sized Scot opening up with a break of 47 before pulling another frame back with a 60. And the unlikely comeback was almost complete with a superb break of 108 with a doubled black to complete his clearance.
Trump was first in for his chance in the decider but missed a black off the spot with his break on 25. But two risky pot attempts from Dott again left the door open and Trump cleared up with a break of 101 to set up an intriguing battle of the left handers against Mark Williams.
In a more one side quarter, a break of 50 proved sufficient for Murphy to take the opener after Bingham missed a costly pink. Murphy got the better of a scrappy second despite missing a black off its spot to hand Bingham a lifeline.
Murphy capitalised on yet more unforced Bingham errors in frame three to forge further ahead and an assured 72 break, again as a result of a poor Bingham safety, put him a frame from victory.
The pattern of errors continued in the next but this time it was Murphy who missed a yellow with the match in his pocket and Bingham for once cleared up to get his name on the board.
But that was as good as it got for an out of sorts Bingham as Murphy produced a break of 79 to march into the semis and surely a much sterner test against Higgins.