Vekic was the first to move through to the final, winning a see-saw battle with No.16 seed Magdalena Rybarikova, 76(5) 16 63. After winning a marathon one-hour, 18-minute first set, Vekic was nearly blanked in the second set by the crafty Rybarikova, but she rebounded in the third to close it out.
"She was playing quite well in the second set and I wasn't playing that well, but the rain delay helped me regroup and my coach told me a few things that helped a lot too," Vekic said. "I just had to work on my serve and be more patient and stay in the points more, and I'm happy I found a way to win.
"I didn't play my best tennis but I'm proud that at the end of the day I won the match."
Vekic is now through to her second WTA final, having finished runner-up at Tashkent last fall.
"In Tashkent I played a lot of matches - I came through the qualies - so I was very, very tired," she said. "I didn't really enjoy the finals there. I was too tired and just too nervous to enjoy it. So tomorrow I'm going to enjoy every second. If I win I win, but I have a lot more years to play and win if I don't."
The last time a player 16 years old or younger won a WTA title was all the way back in 2006, when a 15-year-old Tamira Paszek won Portoroz. Vekic is 16, and just a few weeks shy of her 17th birthday.
Hantuchova followed Vekic into the final with a 57 61 64 win over American qualifier Alison Riske.
"Alison played really well - she always plays well on grass - but I just kept going and kept hanging in there, and tried not to give her too many free points," Hantuchova said. "I was a bit unlucky not to win the first set, I could have won that, but I'm happy with the way I turned it around the next two sets."
"She just played really well," Riske said. "I did the best I could, that's all I could do, but she just played a really clean match. It's always unfortunate to lose, but it's okay because I did all I could do. It's been a long day for me - I put in my first 12-hour work day with all the delays - but all credit to her."
Riske was playing her second WTA semifinal, her first one coming here in 2010. In fact the only other time she made a WTA quarterfinal was here as well, in 2011. Needless to say, she loves Birmingham.
"I'm just really comfortable here, I'm at home," Riske said. "I think that's just for England in general. It's really low key here, the atmosphere is friendly, everything's run well, you don't have any anxiety about anything, everything's taken care of. It's the perfect position to play well and I really love it here."
Hantuchova is in her 15th WTA final, going 5-9 in the first 14. She is playing Vekic for the first time.
"She's having a really good week," the former World No.5 said. "She's beaten some very good players and I think the grass suits her game. She reminds me of myself - a couple of years ago, of course."