Dolonc was down 5-2 in the first set and faced a set point at 5-3, another at 6-5 and two more at 6-4 in the tie-break, but fought back each time and pulled out the set. And with the eighth-seeded Shvedova serving for the second set at 5-4, Dolonc broke, held and broke for the 76(6) 75 victory.
"Yaroslava and I were practicing with each other before the US Open and both of us know each other's games," Dolonc said. "Shvedova is a high-level player and a good server, so I had to be sharp. I was a slow starter and was lucky to get through. I'll need to wake up earlier in my future matches before it's too late!
"It has been six years that I have been playing the Tashkent Open. It has become a tradition for me to play here. I like it here and have good memories. I was a finalist in doubles last year. A title this year would be even more memorable."
Also moving on was Petra Cetkovska, who converted on all five of her break point opportunities in her 62 76(2) defeat of Nigina Abduraimova.
"I'm happy to have gotten through the first round," Cetkovska said. "Compliments to Nigina. She is a talented player and I didn't know what to expect from her. I am pleased with the way I played."
Cetkovska is playing just her sixth WTA main draw this year as she continues her comeback from various injuries.
"I went through a tough time being out for nine months due to a lot of injuries on my knees and foot," Cetkovska said. "It takes time to come back, but now I feel better and stronger with each passing day. My aim is to prevent any more injuries, keep fit and get back to the Top 100 by the end of the year."