World number 14 Bingham overcame David Gilbert 6-2 in the second last-four clash on Saturday evening after Carter had earlier beaten 2015 champion Shaun Murphy 6-3.
Bingham told the BBC: "I was a bit disappointed in my own play, Dave gave me chances in the first three frames and I just took them.
"I got a bit of momentum going I'm just enjoying the moment out there and I'm feeling pretty relaxed."
Gilbert reached the last four of the World Championship last season and fell at the same stage this week.
He told the BBC: "I loved it even though I was playing poorly. I couldn't pot the tough balls and made it easy for Stuart.
"I've got nothing to worry about here, I had a bad day. People might say I'm a nearly man but I used to be the nowhere man so I'm making strides."
World number 17 Carter was only given an invite to the tournament after seven-time winner Ronnie O'Sullivan opted not to take part.
A break of 91 helped him to a 3-1 lead over 2015 champion Murphy and he also hit 70 and 97 to reach his third Triple Crown event final.
"When you get into the competition like I did you think you're on a free roll but when you get here it hits you in the face," Carter told BBC Sport.
"I now think it's mine to lose rather than just being happy to be here, that's my competitive edge.
"It's been a tough few years but I'm still here and still fighting.
"I've been to hell and back and it's special to be in the final but the job is not done yet."
Murphy made two centuries but after failing to build on a break of 56 in the sixth frame Carter went 4-2 ahead before going on to win.
"The way he finished that match off was quite special, it's not easy out there," Murphy told the BBC.
"It was very classily done and I wish him the best in the final."
Tournament schedule and round-by-round results
- All matches up to and including semi-finals best of 11; final best of 19
ROUND ONE
Sunday 12 January
Afternoon Session (1300 - BBC/Eurosport)
- Ding Junhui 3-6 Joe Perry
Evening Session (1900 - BBC/Eurosport)
- Mark Selby 4-6 Ali Carter
Monday 13 January
Afternoon Session (1300 - BBC/Eurosport)
- Neil Robertson 5-6 Stephen Maguire
Evening Session (1900 - BBC/Eurosport)
- Mark Allen 1-6 David Gilbert
Tuesday 14 January
Afternoon Session (1300 - BBC/Eurosport)
- Judd Trump 3-6 Shaun Murphy
Evening Session (1900 - BBC/Eurosport)
- John Higgins 6-1 Barry Hawkins
Wednesday 15 January
Afternoon Session (1300 - BBC/Eurosport)
- Kyren Wilson 6-2 Jack Lisowski
Evening Session (1900 - BBC/Eurosport)
- Mark Williams 2-6 Stuart Bingham
Thursday 16 January
Afternoon Session (1300 - BBC/Eurosport)
- Shaun Murphy 6-3 Joe Perry
Evening Session (1900 - BBC/Eurosport)
- Ali Carter 6-3 John Higgins
Friday 17 January
Afternoon Session (1300 - BBC/Eurosport)
- Stephen Maguire 2-6 David Gilbert
Evening Session (1900 - BBC/Eurosport)
- Kyren Wilson 4-6 Stuart Bingham
Saturday 18 January
Afternoon Session (1300 - BBC/Eurosport)
- Shaun Murphy 3-6 Ali Carter
Evening Session (1900 - BBC/Eurosport)
- David Gilbert 2-6 Stuart Bingham
