The pair met two weeks ago in the last eight in San Jose with Istomin winning 6-2 6-4 but in Florida it was a different story.
Roddick, the fourth seed, struggled on his serve and offered five break opportunities, but Istomin could only take one of them.
And the American former world number one had enough in his tank to secure his second quarter-final appearance of the season.
"I'm feeling better than I did a couple of matches ago," Roddick said. "I served horrendously and still won and was still able to break serve."
Like Roddick, Anderson also suffered an off-day on his serve with a first-serve percentage of just 55 per cent.
Yet nine aces helped him past his Belgian opponent, who has won the tournament in Delray Beach twice before, in 2005 and 2007.
"I thought it really gusty, really windy, and it wasn't easy to get a good rhythm," Anderson said. "I thought it was tough for both of us because we couldn't play the kind of tennis we wanted to play."
In the day's other second round matches, fifth-seed Philipp Kohlschreiber beat Croatia's Ivan Dodig 6-2 6-2 and Dudi Sela saw off Finn Jarko Nieminen 6-4 6-4. The victorious pair will play each other for a place in the semi-finals.
German Kohlschreiber now boasts a record of 12-5 this season, having reached the semi-finals in Auckland and Montpellier.
Sela, of Israel, also bemoaned the adverse weather conditions during his win over Nieminen.
"It was difficult conditions because the wind was swirling," said Sela, who said the weather is similar to what he's used to in Israel.
"It was tough to serve and you had to put your first serves in. I think I served very well and I didn't give him any presents."