Although Acasuso had taken the first set, former champion Roddick looked in command at two sets to one, leading 4-6 6-1 6-2 when the Argentine decided to quit.
World number 70 Acasuso startled Roddick early on but after the American hit back to level, the Argentine had his left knee strapped.
Roddick took advantage by cruising through the third set and, after consulting the trainer again, Acasuso decided he could not continue.
"It's unfortunate Jose hurt his knee. I though he played a very good first set," Roddick said in a courtside interview on his 25th birthday.
"It's not the way you want to get through but at the beginning of the day all you want to do is get through to the third round.
"I felt like I started playing a lot better in the second set so hopefully I can carry that through into the next round."
Roddick, runner-up to Roger Federer here last year, next plays Frenchman Arnaud Clement or former Australian Open champion Thomas Johansson of Sweden.
The American said there may be more life in the men's draw than usual since several potential challengers to Federer's title were in form.
"I feel like some of the top guys, like James (Blake) and Novak (Djokovic) are hitting their stride at the right time, which is giving people maybe a little more to talk about," said Roddick.
The fifth seed was not entirely satisfied with the manner of his victory.
"I don't think you like winning matches like that," said the 2003 champion. "Especially since I felt like I was starting to play OK.
"But at the end of the day your goal is to get through."
