A superb 139 break kept Bingham in his seat in the first frame as Wilson went ahead.
There was a tight 70-60 win in Wilson’s favour to double his lead before Bingham’s break of 69 gave him one back.
Two tight frames saw Wilson grind towards the finish line, one before the restart (65-46) and one after the mid-session interval (71-65).
Then came Bingham’s comeback. He squeaked a 59-53 in the next frame, and breaks of 8 and 75 levelled the scores at four frames a piece.
The crowd witnessed one of the latest games in recent memory when Bingham went ahead for the first time of the night, before another slogfest saw Bingham edge the final frame 69-55 to seal a famous win.
Debutant David Gilbert beat Stephen Maguire 6-2 in an impressive victory in the 2020 Masters.
Gilbert started in exceptional form and laid down the marker with an unanswered 144 break in the first frame.
He then scrapped to go 2-0 up before a break of 91 showed he was capable of keeping his opponent in his chair for length periods.
Maguire then pulled one back thanks to a break of 57, but Gilbert edged a 58-57 win in the fifth frame to go 4-1 up. Another narrow frame victory - 66 to 54 - left Gilbert on the cusp of the semi-finals.
The result was held up when Maguire fell just short of a century break on 94 to bring the score to 5-2.
However Gilbert kept his composure under pressure to take the last frame of the match, and the only man in the competition yet to win a tournament reach the semi-finals.
Gilbert explained that his surprising run at Alexandra Palace has come because he prefers to play in front of a sizeable crowd.
"I think when you've got a big crowd looking at you, waiting for something to happen, good or bad, it is easier for me to control myself, which is strange," he said.
"When I was in the cubicles in Barnsley just before Christmas all I wanted to do was just smash my queue up and walk out.
"My head was totally gone. When you're cueing well and feeling good out there, it's almost easier."
Reaching the final four is the second time Gilbert has reached the semi-final of a Triple Crown event , following on from his run at last year's World Championship.