Selby produced arguably his best level of form since winning his second world title in May with a dominant performance against fellow Englishman Burden.
Breaks of 84, 136 and 102 simply overwhelmed Burden as world number one Selby reached his second straight ranking semi-final after losing to Ding Junhui in the final of the Shanghai Masters last month.
Selby given standing ovation after brilliant century
“The main thing was to win the game. Judd seems to be back to his best so I’m looking forward to playing him.
"It would be great to get to another final.”
1006 Closing moments Trump
Image credit: Eurosport
World number four Trump was equally impressive in completing a 4-0 success against four-times world champion Higgins as runs of 42, 74 and 105 carried him through to the last four in the race for the £67,300 first prize.
Mark Selby makes blistering 136 break
“I didn’t play as well as I did yesterday, I was a bit twitchy when I went 2-0 up,” said Trump.
“I made a nice break in the last frame, and any time you beat John 4-0 you’re doing something right.
Trump completes win over Higgins in style
"I’ve scored heavily this week and not missed much. Mark Selby will be tough, he’s always there in the later stages of tournaments. I’ll have to play my best to beat him."
Tournament favourite Ronnie O'Sullivan was a 4-1 winner against Mark Davis.
O'Sullivan began with a 54 and ended with a 129 while Davis won his only frame of the match with a splendid contribution of 124 in the third frame.
“Mark is a really tough and consistent player so I had to be on my game to win,” said O’Sullivan.
“I started off well then he came back at me and played some good safety, I got a bit lucky as the balls didn’t fall kindly for him and I had to take advantage. I was pleased with my mental performance. These are the type of matches I need to test myself.”
Vintage O'Sullivan reaches European Masters semi-finals
O'Sullivan will face Neil Robertson on Saturday evening for a place in Sunday's final after the Australian ground out a 4-2 win over Anthony McGill on a table that deteriorated the longer the night progressed.
“The table played tough, there has been a lot of rain today so conditions weren’t easy,” said Robertson.
“Anthony played a lot of good safety so it was just a match to get through. The tables will have a new cloth tomorrow so hopefully it will be a better standard. It will be a different match against Ronnie anyway. If I take my chances I can beat him.”