Bingham, who had never lost to Gilbert in 11 previous meetings, put together runs of 94, 71 and 75 to progress to a first Masters final.
"It's fantastic to have the chance [off winning the Masters]. I can't wait. It's what dreams are made of, to be in the final," said Bingham in the studio after the match.
I'm enjoying it out there. Obviously the draw has opened up with most of the seeds being beaten.
And Gilbert, a debutant at the Triple Crown invitational, was - despite an impressive 131 in frame four ahead of the mid-session interval - unable to replicate the form he had shown earlier in the tournament, as the 38-year-old struggled with the pace of the table and his wait to win a ranking tournament goes on.
Gilbert produces break of 131 to cut the arrears
"I tend to do that every time against Stuart, for some reason," said Gilbert after the match.
"Everyone will tell you it was nerves early on - it just wasn't. I couldn't find my lines and was just missing some tricky pots to get myself in.
"After the interval I was really up for it and in the fifth I made a bad cannon when I had a chance to go 3-2 and it could have been different.
I had a fantastic week. It was everything and more that I expected it to be. I wish I was playing tomorrow, but I'll just go home tomorrow.
Earlier, Carter held on to beat Shaun Murphy 6-3 to book his spot in the final.
The Captain compiled runs of 55, 91, 70 and 97 to beat 2005 world champion Murphy to progress.
“I played pretty solid – I missed a couple; you know, how matter you play, you come off and you know if you miss one or two balls, they are the ones you remember,” Carter said in the studio after the match.
Carter, whose performance was a marked improvement on his quarter-final showing against an out-of-sorts John Higgins, added that a conservative, measured approach had served him well.
“I have been playing match snooker all week and it is working, so I am not going to change,” added Carter.
The 40-year-old, only at the invitational Triple Crown event after Ronnie O’Sullivan elected not to play the event, was never behind against the 2015 champion, but had to be at his tenacious best to hold off Murphy, who rattled off breaks of 105, 110 and 56.
Murphy’s exit means that a new face will hold the Paul Hunter Trophy aloft on Sunday, with Bingham also a potential first-time winners.