Paolini had never won a main draw match at Wimbledon before this year, but the world number seven tenaciously saw off Vekic in two hours and 51 minutes on Centre Court to secure a second successive Grand Slam final appearance.
The 28-year-old, who lost the French Open final last month, will face 2022 Wimbledon champion Elena Rybakina or Czech 31st seed Barbora Krejcikova in Saturday's final.
After surviving the emotional encounter with Vekic, Paolini could celebrate becoming the first Italian woman to reach the Wimbledon final.
It has been a breakthrough year for Paolini, who reached her maiden Grand Slam final at Roland Garros before losing to world number one Iga Swiatek.
Paolini, who made the Australia Open last 16 in January, had not gone past the second round in any Slam before this year.
Without a win at the All England Club heading into the tournament, Paolini now has six victories under her belt and has dropped just two sets in the process.
"You know there is no place better than here to fight for every ball and every point," Paolini said.
"I was struggling at the beginning. I was serving really bad, so I'm so happy. This match I will remember forever."
Vekic paid the price for 57 unforced errors, with the semi-final fittingly ending on another wild forehand from the unseeded Croatian.
Unable to contain her frustration at letting 3-1 and 4-3 leads slip in the last set, Vekic broke down in tears in the closing stages of a rollercoaster clash.
Feisty Paolini
Vekic landed the first break in the fifth game of the opening set, taking a 3-2 lead gift-wrapped by two wayward Paolini forehands.
Unloading baseline winners and deft drop-shots at will, the Croatian broke again in the seventh game and emphatically served out the set.
Paolini couldn't convert her first break opportunity of the match in the fourth game of the second set.
But Vekic squandered two break points in the following game, losing her momentum as the feisty Paolini levelled the match with a ferocious forehand to take the set with a break at 5-4.
Vekic took a lengthy break off court to gather herself before the decider, reemerging to break in the first game of the third set.
Yet as the tension mounted, the nervy Croatian stumbled as Paolini broke back to level at 3-3,
Vekic earned another break in the following game before handing Paolini a lifeline by tamely dropping serve for 4-4.
In a dramatic finale, Vekic ignored an apparent injury to save a match point in the 10th game.
When Vekic couldn't take a break point in the next game, she broke down in tears at the change of ends.
Vekic managed to compose herself enough to save a second match point, but she blew a 3-1 lead in the tie-break as Paolini gutted out a memorable victory.
In the day's second semi-final, world number four Rybakina will be chasing a second Wimbledon final appearance.
Krejcikova has a 2-0 record against the Russian-born Kazakh.
