Higgins beat Judd Trump 4-2 in the middle game of three on the night - one extra than usual after last Thursday's event in Penzance was cancelled.
It meant Bingham had to play twice and needed two good results to get near the last four, but he did it in tremendous fashion with two 6-0 whitewashes of world number one Mark Selby and Australian Neil Robertson.
John Higgins also secured his spot in the final four on the night.
Essex potter Bingham enjoyed the night of his life with four centuries in his spell of 12 winning frames on the bounce - taking his earnings for his night's work to £16,000.
"Good day's work isn't it, it'll pay for the wedding," said Bingham. "We're going to Cyprus in May so this will pay for most of that!
"Everyone can do it in practice but to come out and play like that on the main stage is unbelievable. I've just beaten the world number one and a former world champion and I've hammered them really, so if I play like that in the semis I'll be very hard to beat."
Higgins also booked his place in the final four after he beat Trump, with the Scotsman just hitting the one century in his victory.
"I haven't done so well in this event in the past as it's sometimes difficult to play in," said Higgins.
"This time I've just tried to enjoy it. In the past I've got uptight about the shot clock but this year I've had a free run as Ronnie declined his invitation so I'm delighted to be in semis."