María-Teresa Torró-Flor erased second set deficits of 3-0 and 4-2 and converted on seven of eight break point chances in her 61 75 defeat of No.6 seed Begu.
"I knew she would be under pressure to defend the championship," Torró-Flor said. "I remained focused and got a lot of balls in, and she made some mistakes. In the second set I got a bit nervous and went down 3-0, but regained my composure and started playing freely."
As for the fourth-seeded Vekic, she was beaten, 76(4) 63, by Olga Govortsova.
"I've been coming to Tashkent since I was 15," Govortsova said. "I didn't know Donna and had not seen her play, so I just concentrated on my game, which is playing aggressive, and that's what I did."
One of the day's more entertaining matches saw No.3 seed Yvonne Meusburger face 4-0 and 5-3 deficits in the first set and a two-break, 4-1 deficit in the second set yet emerge with a 75 64 triumph over Petra Cetkovska. She has now won 11 of her last 13 matches.
"For me Petra is for sure a Top 30 player," Meusburger said. "Today came down to who was mentally stronger, and in this case it was me."
Top-seeded Bojana Jovanovski was a 62 75 winner over Misaki Doi. The Japanese served for the second set at 5-4, but Jovanovski broke at love, held and broke again to make her first WTA quarterfinal since the first week of the season in Shenzhen.
Also moving on were No.5 seed Alexandra Cadantu, No.7 seed Galina Voskoboeva, Mandy Minella and Nastassja Burnett. Cadantu has surrendered just six games through two matches, best of the field. Burnett is into her first WTA quarterfinal.
The quarterfinals will be played Thursday, with Jovanovski versus Voskoboeva the lone match-up involving two seeded players.