Donaldson, who turns 21 on Monday, saved all eight break points he faced. He broke Cuevas' serve once in each of the last two sets.
The 56th-ranked Donaldson plans to celebrate his birthday by going to Disney Shanghai on Monday, before experiencing a first career meeting against No. 1 Rafael Nadal in the second round.
"I want to get a picture with Mickey, Pluto the dog, and Daffy Duck," Donaldson said, laughing.
On a less lighter note, Donaldson said of playing Nadal: "You want to play against the best and see how your game stacks up. Playing against someone like Rafa is really special. If I lose, it will allow me to know what was my game lacking, what I need to improve on to beat guys like him."
Gilles Simon of France, a 2014 Shanghai finalist, posted a 6-3, 6-4 win over Chinese wild card Wu Yibing, who won the U.S. Open junior boys' title last month.