World No. 74 Watson took 61 minutes on Thursday to get past Croatia's Vekic -- ranked 19 places higher than the Brit -- 6-0 6-4 but had to withstand a late surge.
Watson, who won the Hobart title in 2015, was forced to qualify at this year's event.
But, she has made an impressive run to the final four, knocking out third seed Sorana Cirstea in the opening round.
Watson won the first 11 games of Thursday's match to take a 5-0 lead in the second set and looked on track for an untroubled win until Vekic fired up her forehand and reeled off four-straight games.
"I knew she'd change something and swing freely because you've got nothing to lose at that point," Watson said.
"I just had to stick with her."
But Watson steadied, breaking in the final game.
She'll meet defending champion Elise Mertens for a spot in Saturday's final.
The second seeded Martens advanced on Thursday via a walkover after last year's runner-up Monica Niculescu withdrew due to a shoulder injury.
In the third quarter-final, fifth seed Lesia Tsurenko abruptly ended the impressive run of Romanian teen Aryna Sabalenka 6-1 6-1.
Buzarnescu, ranked No. 57 in the world, took the first set in a tiebreaker, before claiming the second set easily, cruising to a 7-6 (7-5) 6-1 win.
She will play Tsurenko in the other semi-final.