In one of the best matches of the tournament, Paolini missed two match points and was 8-7 behind in the 10-point tie-break before recovering to clinch an incredible victory.
The match lasted two hours 51 minutes, making it the longest women’s singles semi-final at Wimbledon, with the Italian winning 2-6 6-4 7-6 (10-8).
Paolini, who had never won a match at this tournament before this year, said: “I was serving really bad so I am so happy. This match I will remember forever.
“I was just trying to think about what to do on the court, point by point, because I was really in difficulty.”
Paolini lost in the French Open final in May and is the first woman to reach back-to-back Roland Garros and Wimbledon finals since Serena Williams in 2016.
“I think these last months have been crazy for me,” added Paolini.
“I don’t know, I am just trying to focus on what I have to do on court and enjoying what I am doing.
“I love playing tennis.
It is a dream.
I was watching finals when I was a kid at Wimbledon. I am just enjoying it and trying to live in the present.”
Seventh seed Paolini’s victory means she will now face either Kazakhstan’s Elena Rybakina, the 2022 champion, or 31st seed Barbora Krejcikova of the Czech Republic in Saturday’s final.
Those two players meet in the second semi-final on Thursday.
The 28-year-old Italian had lost all three of her matches here before this year, but has now created history – and has a chance of becoming the first Italian player, male or female, to win a Wimbledon singles title.
Paolini had never reached the second week of a Grand Slam until six weeks ago when she made the French Open final.
Croat Vekic, also aiming to reach her first Grand Slam final, stormed through the first set and then led 4-3 with a break of serve in the deciding set, needing only two holds of serve for victory.
But amid sensational scenes on Centre Court, the hugely popular Paolini managed to instantly get the match back on serve.
She failed to convert a match-point chance in the 10th game and then another two games later went to a 10-point tie-break.
Vekic led 8-7 in that, as the lead had constantly changed hands and was two points from victory, but Paolini went ahead and then kept her nerve to seal the win.
