Saturday's final match will result in the first WTA title for either Begu or Vekic. Begu appeared in a pair of finals in 2011 but lost both. Vekic, No. 183 in the world, has never before advanced to a title match.
Begu Friday pulled off her third upset in as many rounds with a 6-3, 6-3 victory over second-seeded Urszula Radwanska. Begu defeated No. 3-seeded Alize Cornet in the second round and eighth-seeded Galina Voskoboeva in Thursday's quarterfinals.
Begu dropped her serve once in each set against Radwanska but piled up three breaks in the first set and two in the second. She won more points (28-27) off Radwanska's serve than Radwanska managed.
Vekic got past Eva Birnerova 6-1, 3-6, 6-1 behind nine aces and winning 68 percent of the points on serve. She had 19 break-point chances and finished off five of them.
Saturday's Tashkent Open winner will take home $37,000 with the runner-up earning $19,000. Radwanska and Birnerova collected $10,200 each as semifinalists.
Caroline Berg Eriksen: Soccer player's wife triggers debate with post-birth selfie
Britney Spears on kissing Ryan Gosling, Justin Timberlake in the Mickey Mouse Club