The 234th-ranked Sanders recorded her career-best win with a defeat of No.131 Irina-Camelia Begu in Brisbane qualifying last week, but way surpassed that with her 62 62 rout of No.39 Peng in which she converted on four of five break point chances and saved all five break point chances on her own serve.
"I haven't been able to wipe the smile off my face yet," Sanders said. "I went out and had nothing to lose. I played really solid and tried to use my forehand as much as possible and didn't make many errors. I just stuck to my game plan and really believed in myself.
"I knew she wasn't just going to go away. She is a really good player. I didn't think too much about the score, I just played every point on its own merit."
The 19-year-old Sanders' competition will get even stiffer in the second round in the form of No.2 seed and World No.19 Kirsten Flipkens.
"It was difficult for us to serve and to move as well," Vesnina said. "I knew it was going to be windy in Hobart and my win last year helped me to understand how to play with the wind. You have to play consistently and be focused throughout the whole match more than when you are playing without wind.
"Definitely experience helped me today. She is a young player and when I was 19, 20, I was playing the wind the same. I was getting frustrated and complaining about the wind. Now, I know what to do."
Securing quarterfinal spots with wins over Australian qualifiers on Tuesday were eighth-seeded Bojana Jovanovski and Alison Riske. From 3-2 in the second set, Jovanovski ran off nine straight games for a 36 62 60 triumph over Olivia Rogowska, and Riske was a 75 46 63 victor over Casey Dellacqua.