Runs of 65 from Bingham and 61 from Selby saw the pair share the opening frames.
However, Bingham reeled off breaks of 83 and 127 to take a two-frame advantage, but, Selby, who survived a scare against Jack Lisowski in his round three match on Thursday, mounted another comeback.
Yet, after cutting the arrears to one frame, it was Bingham who took the sixth frame, courtesy of a break 65.
Trump named Player of the Year for third time in a row
Judd Trump fended off a Mark Allen fightback to progress, courtesy of a 4-3 win.
Judd Trump produces sublime plant
Defending champion Trump produced runs of 58 and 88 on his way to racing into a three-frame lead against world number nine Allen.
However, ‘The Pistol’ responded in style, constructing a 102 in frame four and following that up with a 76 in frame five to cut the arrears.
The 31-year-old came out of a tactical battle in the sixth to level the match but Trump produced a fine 70 to secure passage to the last four.
Elsewhere, Cao Yupeng beat two-time world champion Mark Williams to also make the semi-finals.
Yupeng made breaks of 73 and 76 on his way to downing Williams 4-2.
The last quarter-final of the day saw Zhou Yuelong whitewash Anthony McGill 4-0, with runs of 138 and 136 sealing the win.
EUROPEAN MASTERS RESULTS
Judd Trump 4 – 3 Mark Allen
Cao Yupeng 4 – 2 Mark J Williams
Stuart Bingham 4 - 2 Mark Selby
Zhou Yuelong 4 – 0 Anthony McGill
'Phenomenal Selby stopped Murphy playing in final' - White
'He broke me' - Emotional Murphy on loss to 'super-granite' Selby