Four-time world champion Higgins had twice trailed 3-0 and 7-4 against his Belgian opponent but stormed back to go 7-7 in the evening session.
The Scot rattled off three successive frames to claim victory and will now aim for his 32nd ranking final victory against Robertson, who won a deciding frame 10-9 thriller against Ronnie O'Sullivan in the other semi-final.
"I'm buzzing. I'm really delighted to beat Luca. He started off like a train and at 3-0 behind he could have blown me away really. I couldn't believe I was leading after the first session," Higgins told reporters.
"I feel really good about my game. I'm missing a few balls but the main thing is that deep within myself I'm confident that I can go in and maybe do something. I am going to need to be at the top of my game to have a chance of beating Neil."
Higgins will be gunning for revenge after a 9-8 defeat by Robertson in the English Open final when the pair last met in Milton Keynes last November.
Former world number one Higgins, now in his 30th season as a professional, last beat 'the Thunder from Down' Robertson 13-10 in the quarter-finals of the 2019 world snooker championship.
Robertson beat O'Sullivan 10-4 in the final of the Tour Championship at the Celtic Manor Resort in Wales last year and Higgins said he faces an uphill task to beat the Australian at Venue Cymru in the £150,000 first-to-10-frames clash.
Higgins said: "It is an unbelievable test playing Neil. He stands up there with any snooker player that has played the game. His long potting is unbelievable and he has the whole package, but I will look forward to it."