Kalinina put the Ukrainians in front with a 6-3, 6-4 victory over Tyra Grant before Svitolina sealed victory with a crushing 6-2, 6-2 win against Jasmine Paolini, who had won her last 10 matches in the competition and suffered her first BJK Cup defeat since 2024.
Ukraine will take on a strong Czech Republic team, spearheaded by this year's Wimbledon finalists Linda Noskova and Karolina Muchova, in Sunday's championship match at the Shenzhen Bay Sports Centre.
"Definitely unbelievable to be fair," said Svitolina, who lost to Paolini at the same stage of the competition 12 months ago.
"I was trying to be really focused. It was a really tough loss for me last year here, so I really had to be focused and really step up my game."
Svitolina has been providing financial and operational support for the Ukrainian national team for the past three years through her foundation.
"It's a really special moment for us, for Ukraine, going through difficult times back home, all the people. It's just unbelievable to get for the first time in the finals here," she added.
In a rematch of last year's semi-final, Ukraine turned the tables on a team that was looking to reach a fourth consecutive final and clinch a third straight title.
After claiming two points for Ukraine with singles and doubles victories against Belgium two days earlier, Kalinina, the world number 48, needed just 86 minutes to overcome a 150th-ranked Grant, who was making her competition debut for Italy.
Svitolina then stepped on court with a purpose, keen to avoid another defeat after losing her singles clash in Ukraine's 2-1 quarter-final victory over Belgium on Thursday.
The world number seven leapt to a double-break lead over Paolini, who briefly cut the deficit but could not hold off a near-flawless Svitolina in the 31-minute opening set.
Svitolina was in cruise control as she took a seventh game in a row to surge ahead 4-0 in the second set.
Paolini briefly stopped the bleeding in game five but looked beaten as she sat at the Italy bench at the changeover, a towel hanging over her head, covering her face in despair.
The tie was over three games later as Svitolina fired one winner after the other to claim the 20th BJK Cup win of her career and send Ukraine into a first-ever final.